diff --git a/changelog b/changelog index 9fd4a40..e684837 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,9 @@ +20130727 tpd src/axiom-website/patches.html 20130727.01.tpd.patch +20130727 tpd src/axiom-website/CATS/index.html add rich3c +20130727 tpd src/axiom-website/CATS/rich3c.input added +20130727 tpd src/axiom-website/CATS/rich3c.input.pdf added +20130727 tpd src/input/Makefile add rich3c +20130727 tpd src/input/rich3c.input added 20130726 tpd src/axiom-website/patches.html 20130726.01.tpd.patch 20130726 tpd src/axiom-website/CATS/index.html add rich3b 20130726 tpd src/axiom-website/CATS/rich3b.input added diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index ad1f519..7303013 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -302,6 +302,9 @@ They have been rewritten using Axiom syntax. (a+b x)^m (c+d)^n (e+f x)^p (part 2) source pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 3) + source + pdf


Rich



diff --git a/src/axiom-website/CATS/rich3c.input.pamphlet b/src/axiom-website/CATS/rich3c.input.pamphlet new file mode 100644 index 0000000..88bdf31 --- /dev/null +++ b/src/axiom-website/CATS/rich3c.input.pamphlet @@ -0,0 +1,6734 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file +\item 100 supplied "optimal results" +\item 25 matching answers +\item 12 answers that differ from the optimal results +\item 58 cases that Axiom failed to integrate +\item 5 that contain expressions Axiom does not recognize +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3c.output +)spool rich3c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=x^5/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 5 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=5/4*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+1/2*a*(b*c-5*a*d)*x^3/(b^2*d*_ + (b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+1/2*x^4/(b*d*(c+d*x)^(3/2)*_ + sqrt(a+b*x))+1/6*c*(7*b^2*c^2-6*a*b*c*d+15*a^2*d^2)*x^2*_ + sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^2*(c+d*x)^(3/2))+1/6*_ + c*(4*a*c*(7*b^2*c^2-6*a*b*c*d+15*a^2*d^2)+(35*b^3*c^3-_ + 33*a*b^2*c^2*d-15*a^2*b*c*d^2+45*a^3*d^3)*x)*sqrt(a+b*x)/_ + (b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x))-1/12*(3*b*c-a*d)*_ + (35*b^3*c^3-33*a*b^2*c^2*d-15*a^2*b*c*d^2+45*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d +--R + +--R 5 5 +--R - 105b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R 45a c d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (- 15a b d + 24a b c d + 18a b c d - 48a b c d + 21b c d )x +--R + +--R 5 6 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (- 45a d + 66a b c d + 12a b c d - 237a b c d + 140b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 90a c d + 45a b c d + 84a b c d - 222a b c d - 50a b c d +--R + +--R 5 6 +--R 105b c +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 45a c d + 30a b c d + 36a b c d - 190a b c d + 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 3 8 2 4 7 5 2 6 6 3 5 3 3 7 +--R (12a b d - 36a b c d + 36a b c d - 12b c d )x + 12a b c d +--R + +--R 2 4 2 6 5 3 5 6 4 4 +--R - 36a b c d + 36a b c d - 12b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=x^4/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 4 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-(5*b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(5/2)*d^(7/2))+a*(b*c-3*a*d)*x^2/(b^2*d*(b*c-a*d)*(c+d*x)^(3/2)*_ + sqrt(a+b*x))+x^3/(b*d*(c+d*x)^(3/2)*sqrt(a+b*x))+1/3*c*_ + (4*a*c*(b*c-3*a*d)+(b*c-a*d)*(5*b*c+3*a*d)*x)*sqrt(a+b*x)/_ + (b^2*d^2*(b*c-a*d)^2*(c+d*x)^(3/2))+1/3*c*(15*b^3*c^3-_ + 35*a*b^2*c^2*d+25*a^2*b*c*d^2-21*a^3*d^3)*sqrt(a+b*x)/_ + (b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c d)x - 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 18a b c d - 36a b c d + 15b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (9a d - 3a b c d - 9a b c d + 39a b c d - 20b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (18a c d - 15a b c d + 33a b c d + 11a b c d - 15b c )x + 9a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 9a b c d + 31a b c d - 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 2 7 2 3 6 4 2 5 5 3 4 3 2 6 2 3 2 5 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 4 3 4 5 4 3 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=x^3/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 3 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))-_ + 2*x^3/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+8/3*c*x^2*sqrt(a+b*x)/_ + ((b*c-a*d)^2*(c+d*x)^(3/2))+4/3*c*(8*a*c+(b*c+3*a*d)*x)*_ + sqrt(a+b*x)/(d*(b*c-a*d)^3*sqrt(c+d*x))-2/3*(3*b*c-a*d)*_ + (b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 18a b c d + 18a b c d - 6b c d)x + 6a c d - 18a b c d +--R + +--R 2 3 3 4 +--R 18a b c d - 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 4 2 2 2 3 3 2 +--R (- 6a d - 18a b c d + 8b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 +--R (- 12a c d - 18a b c d - 8a b c d + 6b c )x - 6a c d - 16a b c d +--R + +--R 2 4 +--R 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 6 2 2 5 3 2 4 4 3 3 3 5 2 2 2 4 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 3 3 3 4 4 2 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=x^2/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-2*a^2/(b^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*(b^2*c^2+3*a^2*d^2)*_ + sqrt(a+b*x)/(b^2*d*(b*c-a*d)^2*(c+d*x)^(3/2))+_ + 2/3*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^3*_ + sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (6a d + 12a b c d - 2b c )x + (24a c d + 8a b c )x + 16a c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R ((30a d + 60a b c d - 10b c )x + (120a c d + 40a b c )x + 80a c ) +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 3 2 3 2 2 2 2 +--R (8a b c + 200a b)d x + ((8a c + 200a )d + (16a b c + 400a b c)d)x +--R + +--R 2 2 3 3 2 2 2 3 3 2 +--R ((16a c + 400a c)d + 8a b c + 200a b c )x + 8a c + 200a c +--R / +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (15a b d - 45a b c d + 45a b c d - 15b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 15a b c d - 45a b c d + 75a b c d - 30b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (30a c d - 75a b c d + 45a b c d + 15a b c d - 15b c )x + 15a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 45a b c d + 45a b c d - 15a b c +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 +--R 8a c + 200a +--R (4) ---------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R 15a d - 45a b c d + 45a b c d - 15b c +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=x/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=2*a/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b*c+3*a*d)*_ + sqrt(a+b*x)/(b*(b*c-a*d)^2*(c+d*x)^(3/2))+4/3*(b*c+3*a*d)*_ + sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (- 12a b d - 4b c d)x + (- 6a d - 20a b c d - 6b c )x - 4a c d +--R + +--R 2 +--R - 12a b c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 3 +--R (- 36a b c d - 12b c d)x + (- 18a c d - 60a b c d - 18b c )x +--R + +--R 2 2 3 +--R - 12a c d - 36a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 3 2 2 2 2 3 +--R ((- 2a b c - 18a b)d + (- 6b c - 54a b c)d )x +--R + +--R 2 3 3 2 2 2 +--R (- 2a c - 18a )d + (- 10a b c - 90a b c)d +--R + +--R 2 3 2 2 +--R (- 12b c - 108a b c )d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 2 4 2 3 +--R ((- 4a c - 36a c)d + (- 14a b c - 126a b c )d - 6b c - 54a b c )x +--R + +--R 2 3 3 2 4 2 3 +--R (- 2a c - 18a c )d - 6a b c - 54a b c +--R / +--R 3 5 2 2 2 4 3 3 3 4 4 2 3 +--R (9a b c d - 27a b c d + 27a b c d - 9b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 2 +--R (9a c d - 9a b c d - 27a b c d + 45a b c d - 18b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4 3 3 +--R (18a c d - 45a b c d + 27a b c d + 9a b c d - 9b c )x + 9a c d +--R + +--R 3 4 2 2 2 5 3 6 +--R - 27a b c d + 27a b c d - 9a b c +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R (- 2a c - 18a )d - 6b c - 54a b c +--R (4) ---------------------------------------- +--R 3 3 2 2 2 2 3 3 4 +--R 9a c d - 27a b c d + 27a b c d - 9b c +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=1/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=(-2)/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-_ + 8/3*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(3/2))-_ + 16/3*b*d*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R 16b d x + (8a b d + 24b c d)x - 2a d + 12a b c d + 6b c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 3 3 2 2 2 3 +--R 64a b c d x + (32a b c d + 96a b c d)x - 8a c d + 48a b c d +--R + +--R 2 4 +--R 24a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 3 4 2 2 2 2 3 3 3 3 2 2 3 +--R ((- a b c - 16a b)d + (6a b c + 96a b c)d + (3b c + 48a b c )d )x +--R + +--R 3 4 4 2 2 3 3 2 3 2 2 2 2 +--R (- a c - 16a )d + (4a b c + 64a b c)d + (15a b c + 240a b c )d +--R + +--R 3 4 3 3 +--R (6b c + 96a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 2a c - 32a c)d + (11a b c + 176a b c )d +--R + +--R 2 4 2 2 3 3 5 3 4 +--R (12a b c + 192a b c )d + 3b c + 48a b c +--R * +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 2 5 2 2 4 +--R (- a c - 16a c )d + (6a b c + 96a b c )d + 3a b c + 48a b c +--R / +--R 4 2 5 3 2 3 4 2 3 4 3 4 5 2 3 +--R (12a b c d - 36a b c d + 36a b c d - 12a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (12a c d - 12a b c d - 36a b c d + 60a b c d - 24a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (24a c d - 60a b c d + 36a b c d + 12a b c d - 12a b c )x + 12a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R - 36a b c d + 36a b c d - 12a b c +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (- a c - 16a )d + (6a b c + 96a b c)d + 3b c + 48a b c +--R (4) ---------------------------------------------------------- +--R 4 2 3 3 3 2 2 2 4 3 5 +--R 12a c d - 36a b c d + 36a b c d - 12a b c +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=1/(x*(a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 2 4 2 3 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))+_ + 2*b/(a*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 2/3*d*(3*b*c+a*d)*sqrt(a+b*x)/(a*c*(b*c-a*d)^2*(c+d*x)^(3/2))+_ + 2/3*d*(3*b*c-a*d)*(b*c+3*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c d)x - 6a c d + 18a b c d +--R + +--R 2 3 3 4 +--R - 18a b c d + 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 2 3 3 2 2 2 +--R (6a b d - 16a b c d - 6b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 8a b c d - 18a b c d - 12b c d)x + 8a c d - 18a b c d +--R + +--R 3 4 +--R - 6b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x + 3a c d - 9a b c d +--R + +--R 2 2 5 3 6 +--R 9a b c d - 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=1/(x^2*(a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=(3*b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (a^(5/2)*c^(7/2))-b*(3*b*c-a*d)/(a^2*c*(b*c-a*d)*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+(-1)/(a*c*x*(c+d*x)^(3/2)*sqrt(a+b*x))-_ + 1/3*d*(9*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)/(a^2*_ + c^2*(b*c-a*d)^2*(c+d*x)^(3/2))-1/3*d*(9*b^3*c^3-9*a*_ + b^2*c^2*d+31*a^2*b*c*d^2-15*a^3*d^3)*sqrt(a+b*x)/(a^2*_ + c^3*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (15a c d - 36a b c d + 18a b c d + 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 15a b d + 31a b c d - 9a b c d + 9b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 15a d + 11a b c d + 33a b c d - 15a b c d + 18b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 20a c d + 39a b c d - 9a b c d - 3a b c d + 9b c )x - 3a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=1/(x^3*(a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 6 2 5 2 4 2 3 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=-5/4*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_ + (sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))+1/4*b*(15*b^2*c^2-_ + 7*a^2*d^2)/(a^3*c^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + (-1/2)/(a*c*x^2*(c+d*x)^(3/2)*sqrt(a+b*x))+1/4*(5*b*c+7*a*d)/_ + (a^2*c^2*x*(c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(45*b^3*c^3-_ + 15*a*b^2*c^2*d-33*a^2*b*c*d^2+35*a^3*d^3)*sqrt(a+b*x)/_ + (a^3*c^3*(b*c-a*d)^2*(c+d*x)^(3/2))+1/12*d*(45*b^4*c^4-_ + 30*a*b^3*c^3*d-36*a^2*b^2*c^2*d^2+190*a^3*b*c*d^3-105*a^4*d^4)*_ + sqrt(a+b*x)/(a^3*c^4*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R - 105a d + 225a b c d - 90a b c d - 30a b c d - 45a b c d +--R + +--R 5 5 +--R 45b c d +--R * +--R 3 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 105a c d + 225a b c d - 90a b c d - 30a b c d - 45a b c d +--R + +--R 5 6 +--R 45b c +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 4 +--R (105a b d - 190a b c d + 36a b c d + 30a b c d - 45b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 105a d - 50a b c d - 222a b c d + 84a b c d + 45a b c d +--R + +--R 5 5 +--R - 90b c d +--R * +--R 3 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 6 2 +--R (140a c d - 237a b c d + 12a b c d + 66a b c d - 45b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R (21a c d - 48a b c d + 18a b c d + 24a b c d - 15a b c )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 4 4 5 5 3 4 2 6 2 3 3 7 3 +--R (12a c d - 36a b c d + 36a b c d - 12a b c d)x +--R + +--R 6 5 3 5 6 2 4 2 7 3 3 8 2 +--R (12a c d - 36a b c d + 36a b c d - 12a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 500 +--m0:=a0-r0 +--E 44 + +--S 45 of 500 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 500 +t0:=x^4*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 6 5 2 4 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=-2/3*x^4*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+1/128*(b*c-a*d)*_ + (3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*_ + b*c*d^3+3003*a^4*d^4)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(c+d*x)))/(b^(15/2)*d^(5/2))-2/3*(8*b*c-13*a*d)*_ + x^3*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))+1/192*_ + (3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*_ + b*c*d^3+3003*a^4*d^4)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^6*d^2*_ + (b*c-a*d))-1/240*(15*b^3*c^3+125*a*b^2*c^2*d-2343*a^2*_ + b*c*d^2+3003*a^3*d^3)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^5*d^2*_ + (b*c-a*d))+1/120*(15*b^2*c^2-902*a*b*c*d+1287*a^2*d^2)*_ + x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))+1/15*(93*_ + b*c-143*a*d)*x^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))+_ + 1/128*(3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-_ + 2772*a^3*b*c*d^3+3003*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^7*d^2) +--R +--R +--R (2) +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R - 45045a b d + 86625a b c d - 47250a b c d + 5250a b c d +--R + +--R 5 4 6 5 +--R 375a b c d + 45b c +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 +--R - 45045a d + 86625a b c d - 47250a b c d + 5250a b c d +--R + +--R 2 4 4 5 5 +--R 375a b c d + 45a b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 6 4 6 5 4 6 3 5 +--R 384b d x + (- 624a b d + 1008b c d )x +--R + +--R 2 4 4 5 3 6 2 2 4 +--R (1144a b d - 1888a b c d + 744b c d )x +--R + +--R 3 3 4 2 4 3 5 2 2 6 3 3 +--R (- 2574a b d + 4378a b c d - 1834a b c d + 30b c d)x +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (9009a b d - 16038a b c d + 7404a b c d - 330a b c d - 45b c )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 +--R 60060a b d - 97482a b c d + 38646a b c d - 750a b c d +--R + +--R 5 4 +--R - 90a b c +--R * +--R x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 45045a d - 71610a b c d + 27384a b c d - 390a b c d - 45a b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R / +--R 8 2 7 2 +-+ +-+ +-------+ +--R (1920b d x + 1920a b d )\|b \|d \|b x + a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 500 +--m0:=a0-r0 +--E 49 + +--S 50 of 500 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 500 +t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-2/3*x^3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))-5/64*(b*c-a*d)*_ + (b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(13/2)*d^(3/2))-_ + 2/3*(6*b*c-11*a*d)*x^2*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-_ + 5/96*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_ + (c+d*x)^(3/2)*sqrt(a+b*x)/(b^5*d*(b*c-a*d))+1/24*(5*b^2*c^2-_ + 156*a*b*c*d+231*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))+_ + 1/12*(59*b*c-99*a*d)*x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))-_ + 5/64*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^6*d) +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (3465a b d - 6300a b c d + 3150a b c d - 300a b c d - 15b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3465a d - 6300a b c d + 3150a b c d - 300a b c d - 15a b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 3 5 4 3 5 2 4 +--R 48b d x + (- 88a b d + 136b c d )x +--R + +--R 2 3 3 4 2 5 2 3 +--R (198a b d - 316a b c d + 118b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 693a b d + 1161a b c d - 483a b c d + 15b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (- 4620a b d + 7014a b c d - 2472a b c d + 30a b c )x - 3465a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 5145a b c d - 1743a b c d + 15a b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R / +--R 7 6 +-+ +-+ +-------+ +--R (192b d x + 192a b d)\|b \|d \|b x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 500 +--m0:=a0-r0 +--E 54 + +--S 55 of 500 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 500 +t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=-2/3*a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+_ + 5/8*(b*c-a*d)*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*sqrt(d))+_ + 4/3*a*(3*b*c-5*a*d)*(c+d*x)^(7/2)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))+_ + 5/12*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/_ + (b^4*(b*c-a*d))+1/3*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(5/2)*_ + sqrt(a+b*x)/(b^3*(b*c-a*d)^2)+5/8*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 315a b d + 525a b c d - 225a b c d + 15b c )x - 315a d +--R + +--R 3 2 2 2 2 3 3 +--R 525a b c d - 225a b c d + 15a b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 2 4 3 2 4 3 +--R 8b d x + (- 18a b d + 26b c d)x +--R + +--R 2 2 2 3 4 2 2 +--R (63a b d - 96a b c d + 33b c )x +--R + +--R 3 2 2 2 3 2 4 2 3 +--R (420a b d - 574a b c d + 162a b c )x + 315a d - 420a b c d +--R + +--R 2 2 2 +--R 113a b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R / +--R 6 5 +-+ +-+ +-------+ +--R (24b x + 24a b )\|b \|d \|b x + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=x*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +--R (d x + 2c d x + c x)\|d x + c +--R (1) -------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=2/3*a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x)^(3/2))+5/4*(3*b*c-7*a*d)*_ + (b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(d)/b^(9/2)-2/3*(3*b*c-7*a*d)*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*_ + sqrt(a+b*x))+5/6*d*(3*b*c-7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/_ + (b^3*(b*c-a*d))+5/4*d*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((105a b d - 150a b c d + 45b c )x + 105a d - 150a b c d + 45a b c ) +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R \|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 3 2 2 3 2 +--R 6b d x + (- 21a b d + 27b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 140a b d + 158a b c d - 24b c )x - 105a d + 115a b c d - 16a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 5 4 +-+ +-------+ +--R (12b x + 12a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-2/3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+5*d^(3/2)*(b*c-a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-_ + 10/3*d*(c+d*x)^(3/2)/(b^2*sqrt(a+b*x))+5*d^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 +-+ +-------+ +--R ((- 15a b d + 15b c d)x - 15a d + 15a b c d)\|d \|b x + a +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (3b d x + (20a b d - 14b c d)x + 15a d - 10a b c d - 2b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(c+d*x)^(5/2)/(x*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) -------------------------------- +--R 2 3 2 2 +-------+ +--R (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=2/3*(c+d*x)^(5/2)/(a*(a+b*x)^(3/2))-2*c^(5/2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(5/2)+2*d^(5/2)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)+_ + 2/3*(3*b*c+2*a*d)*(c+d*x)^(3/2)/(a^2*b*sqrt(a+b*x))-_ + 2*d*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*b^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 3 2 +-+ +-+ +-------+ \|d \|b x + a +--R (6a b d x + 6a d )\|a \|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 3 2 2 2 +-+ +-+ +-------+ \|c \|b x + a +--R (- 6b c x - 6a b c )\|b \|c \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 3 2 3 2 2 2 2 +-+ +-+ +--R ((- 8a b d + 2a b c d + 6b c )x - 6a d - 2a b c d + 8a b c )\|a \|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 3 3 2 +-+ +-+ +-------+ +--R (3a b x + 3a b )\|a \|b \|b x + a +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-5/3*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x)^(3/2))-(c+d*x)^(5/2)/_ + (a*x*(a+b*x)^(3/2))+5*c^(3/2)*(b*c-a*d)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(7/2)-5*c*(b*c-a*d)*_ + sqrt(c+d*x)/(a^3*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 +-+ +-------+ +--R ((- 15a b c d + 15b c )x + (- 15a c d + 15a b c )x)\|c \|b x + a +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R ((2a d + 10a b c d - 15b c )x + (14a c d - 20a b c )x - 3a c )\|a +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 2 4 +-+ +-------+ +--R (3a b x + 3a x)\|a \|b x + a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 5 4 2 3 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=1/4*(7*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x)^(3/2))-1/2*(c+d*x)^(5/2)/_ + (a*x^2*(a+b*x)^(3/2))-5/4*(7*b*c-3*a*d)*(b*c-a*d)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(9/2)+_ + 1/12*(35*b*c-29*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*(a+b*x)^(3/2))+_ + 1/12*(105*b^2*c^2-115*a*b*c*d+16*a^2*d^2)*sqrt(c+d*x)/(a^4*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 +--R (- 45a b d + 150a b c d - 105b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 45a d + 150a b c d - 105a b c )x +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|c \|b x + a +--R \|c \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 3 2 3 +--R (16a b d - 115a b c d + 105b c )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (24a d - 158a b c d + 140a b c )x + (- 27a c d + 21a b c )x - 6a c +--R * +--R +-+ +-------+ +--R \|a \|d x + c +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x + 12a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 6 5 2 4 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=1/12*(9*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x)^(3/2))-_ + 1/3*(c+d*x)^(5/2)/(a*x^3*(a+b*x)^(3/2))+5/8*(b*c-a*d)*_ + (21*b^2*c^2-14*a*b*c*d+a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_ + (sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*sqrt(c))-7/24*b*(15*b*c-7*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/(a^4*(a+b*x)^(3/2))-1/8*(21*b*c-5*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/(a^3*x*(a+b*x)^(3/2))-_ + 1/24*b*(315*b^2*c^2-420*a*b*c*d+113*a^2*d^2)*sqrt(c+d*x)/(a^5*sqrt(a+b*x)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 225a b c d - 525a b c d + 315b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 225a b c d - 525a b c d + 315a b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 3 4 2 4 +--R (- 113a b d + 420a b c d - 315b c )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 162a b d + 574a b c d - 420a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 96a b c d - 63a b c )x + (- 26a c d + 18a b c )x - 8a c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +-+ +-------+ +--R (24a b x + 24a x )\|a \|c \|b x + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(c+d*x)^(5/2)/(x^5*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 7 6 2 5 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=1/24*(11*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^3*(a+b*x)^(3/2))-_ + 1/4*(c+d*x)^(5/2)/(a*x^4*(a+b*x)^(3/2))-5/64*(b*c-a*d)*_ + (231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*_ + atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(13/2)*_ + c^(3/2))+1/64*b*(b*c-a*d)*(385*b^2*c^2-238*a*b*c*d+5*_ + a^2*d^2)*sqrt(c+d*x)/(a^5*c*(a+b*x)^(3/2))-1/32*(33*b*c-_ + 5*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*x^2*(a+b*x)^(3/2))+_ + 1/64*(b*c-a*d)*(231*b^2*c^2-156*a*b*c*d+5*a^2*d^2)*_ + sqrt(c+d*x)/(a^4*c*x*(a+b*x)^(3/2))+1/64*b*(1155*b^3*c^3-_ + 1715*a*b^2*c^2*d+581*a^2*b*c*d^2-5*a^3*d^3)*sqrt(c+d*x)/_ + (a^6*c*sqrt(a+b*x)) +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (15a b d + 300a b c d - 3150a b c d + 6300a b c d - 3465b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (15a d + 300a b c d - 3150a b c d + 6300a b c d - 3465a b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 15a b d + 1743a b c d - 5145a b c d + 3465b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 30a b d + 2472a b c d - 7014a b c d + 4620a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 15a d + 483a b c d - 1161a b c d + 693a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 +--R (- 118a c d + 316a b c d - 198a b c )x + (- 136a c d + 88a b c )x +--R + +--R 5 3 +--R - 48a c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R / +--R 6 5 7 4 +-+ +-+ +-------+ +--R (192a b c x + 192a c x )\|a \|c \|b x + a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=x^2/((a+b*x)^(5/2)*(c+d*x)^(1/2)) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (b x + 2a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))-_ + 2/3*a^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+_ + 4/3*a*(3*b*c-2*a*d)*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((6a b d - 12a b c d + 6b c )x + 6a d - 12a b c d + 6a b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 3 2 +-+ +-+ +-------+ +--R ((- 8a b d + 12a b c)x - 6a d + 10a b c)\|b \|d \|d x + c +--R / +--R 2 3 2 4 5 2 3 2 2 2 3 4 2 +-+ +-+ +--R ((3a b d - 6a b c d + 3b c )x + 3a b d - 6a b c d + 3a b c )\|b \|d +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=x^6/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=1/6*a*(3*b*c-7*a*d)*x^4/(b^2*d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_ + 1/2*x^5/(b*d*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5/4*(7*b^2*c^2+_ + 10*a*b*c*d+7*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))+1/6*a*_ + (3*b^2*c^2-62*a*b*c*d+35*a^2*d^2)*x^3/(b^3*d*(b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+1/6*c*(7*b^3*c^3-9*a*b^2*c^2*d+_ + 69*a^2*b*c*d^2-35*a^3*d^3)*x^2*sqrt(a+b*x)/(b^3*d^2*(b*c-a*d)^3*_ + (c+d*x)^(3/2))+1/6*c*(4*a*c*(7*b^3*c^3-9*a*b^2*c^2*d+_ + 69*a^2*b*c*d^2-35*a^3*d^3)+(35*b^4*c^4-48*a*b^3*c^3*d-_ + 18*a^2*b^2*c^2*d^2+200*a^3*b*c*d^3-105*a^4*d^4)*x)*_ + sqrt(a+b*x)/(b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x))-_ + 1/12*(3*b*c-a*d)*(35*b^4*c^4-48*a*b^3*c^3*d-18*a^2*b^2*c^2*d^2+_ + 200*a^3*b*c*d^3-105*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4*(b*c-a*d)^4) +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 105a b d - 270a b c d + 135a b c d + 60a b c d + 135a b c d +--R + +--R 6 5 2 7 6 +--R - 270a b c d + 105b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 105a d - 165a b c d - 135a b c d + 195a b c d + 195a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 135a b c d - 165a b c d + 105b c +--R * +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R 105a c d - 270a b c d + 135a b c d + 60a b c d + 135a b c d +--R + +--R 2 5 6 6 7 +--R - 270a b c d + 105a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 5 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 21a b d + 63a b c d - 42a b c d - 42a b c d + 63a b c d +--R + +--R 7 5 2 +--R - 21b c d +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 140a b d + 276a b c d + 12a b c d - 168a b c d + 12a b c d +--R + +--R 6 5 2 7 6 +--R 276a b c d - 140b c d +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 105a d - 45a b c d + 549a b c d - 207a b c d - 207a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 549a b c d - 45a b c d - 105b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R - 210a c d + 330a b c d + 186a b c d - 228a b c d +--R + +--R 3 4 5 2 2 5 6 6 7 +--R 186a b c d + 330a b c d - 210a b c +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R - 105a c d + 235a b c d - 66a b c d - 66a b c d + 235a b c d +--R + +--R 2 5 7 +--R - 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 9 4 5 2 +--R (12a b d - 48a b c d + 72a b c d - 48a b c d + 12b c d )x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 +--R 12a b d - 36a b c d + 24a b c d + 24a b c d - 36a b c d +--R + +--R 9 5 4 +--R 12b c d +--R * +--R x +--R + +--R 5 4 8 4 5 2 7 3 6 3 6 2 7 4 5 8 5 4 +--R 12a b c d - 48a b c d + 72a b c d - 48a b c d + 12a b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=x^5/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=1/3*a*(3*b*c-5*a*d)*x^3/(b^2*d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_ + x^4/(b*d*(a+b*x)^(3/2)*(c+d*x)^(3/2))-5*(b*c+a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+_ + a*(b^2*c^2-10*a*b*c*d+5*a^2*d^2)*x^2/(b^3*d*(b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+1/3*c*(4*a*c*(b^2*c^2-10*a*b*c*d+_ + 5*a^2*d^2)+5*(b*c-a*d)^2*(b*c+a*d)*x)*sqrt(a+b*x)/(b^3*d^2*_ + (b*c-a*d)^3*(c+d*x)^(3/2))+1/3*c*(15*b^4*c^4-44*a*b^3*c^3*d+_ + 62*a^2*b^2*c^2*d^2-100*a^3*b*c*d^3+35*a^4*d^4)*sqrt(a+b*x)/_ + (b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b d + 45a b c d - 30a b c d - 30a b c d + 45a b c d +--R + +--R 6 5 +--R - 15b c d +--R * +--R 2 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 15a d + 30a b c d + 15a b c d - 60a b c d + 15a b c d +--R + +--R 5 5 6 6 +--R 30a b c d - 15b c +--R * +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 15a c d + 45a b c d - 30a b c d - 30a b c d + 45a b c d +--R + +--R 5 6 +--R - 15a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 20a b d - 48a b c d + 12a b c d + 12a b c d - 48a b c d +--R + +--R 6 5 +--R 20b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (15a d - 87a b c d + 48a b c d - 87a b c d + 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 30a c d - 60a b c d - 18a b c d - 18a b c d - 60a b c d +--R + +--R 5 6 +--R 30a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 15a c d - 40a b c d + 18a b c d - 40a b c d + 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 +--R (3a b d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c d )x +--R + +--R 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 7 5 3 +--R 3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=x^4/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=-2/3*x^4/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_ + 4/3*(4*b*c-a*d)*x^3/(b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 4/3*c*(5*b*c-a*d)*x^2*sqrt(a+b*x)/(b*(b*c-a*d)^3*(c+d*x)^(3/2))+_ + 4/3*c*(4*a*c*(5*b*c-a*d)+(b^2*c^2+10*a*b*c*d-3*a^2*d^2)*x)*_ + sqrt(a+b*x)/(b*d*(b*c-a*d)^4*sqrt(c+d*x))-2/3*(3*b*c-a*d)*_ + (b^2*c^2+10*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_ + (b^2*d^2*(b*c-a*d)^4) +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 6a c d - 24a b c d + 36a b c d - 24a b c d + 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 8a b d + 24a b c d + 24a b c d - 8b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 6a d + 6a b c d + 48a b c d + 48a b c d + 6a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 12a c d + 36a b c d + 48a b c d + 36a b c d - 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 22a b c d + 22a b c d - 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 +--R (3a b d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c d )x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=x^3/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=-2/3*x^3/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-4*a^2*c/_ + (b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-4/3*c*_ + (b^2*c^2+3*a^2*d^2)*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^3*(c+d*x)^(3/2))+_ + 4/3*c*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^4*_ + sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (2a d - 18a b c d - 18a b c d + 2b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 12a c d - 72a b c d - 12a b c )x + (- 48a c d - 48a b c )x - 32a c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 +--R (2a d - 18a b c d - 18a b c d + 2b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 +--R (- 12a c d - 72a b c d - 12a b c )x + (- 48a c d - 48a b c )x +--R + +--R 3 3 +--R - 32a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 2 2 2 4 +--R (16a b c + 16a b c)d x +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R ((32a b c + 32a b c)d + (32a b c + 32a b c )d)x +--R + +--R 3 2 4 2 2 3 3 2 2 4 2 2 3 2 +--R ((16a c + 16a c)d + (64a b c + 64a b c )d + 16a b c + 16a b c )x +--R + +--R 3 3 4 2 2 4 3 3 3 4 4 3 +--R ((32a c + 32a c )d + 32a b c + 32a b c )x + 16a c + 16a c +--R / +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3 +--R (6a b d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6b c d)x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (3a d - 27a b c d + 48a b c d - 27a b c d + 3b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (6a c d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6a b c )x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R 16a c + 16a c +--R (4) --------------------------------------------------- +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3a d - 12a b c d + 18a b c d - 12a b c d + 3b c +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=x^2/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=-2/3*a^2/(b^2*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*a*c/_ + (b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b^2*c^2+_ + 6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b^2*(b*c-a*d)^3*(c+d*x)^(3/2))+_ + 4/3*(b^2*c^2+6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 +--R (4a b d + 24a b c d + 4b c d)x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d + 42a b c d + 42a b c d + 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 2 3 +--R (24a c d + 48a b c d + 24a b c )x + 16a c d + 16a b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 +--R (12a b d + 72a b c d + 12b c d)x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (18a d + 126a b c d + 126a b c d + 18b c )x +--R + +--R 3 2 2 2 2 3 3 2 2 3 +--R (72a c d + 144a b c d + 72a b c )x + 48a c d + 48a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 2 3 3 2 3 2 4 +--R ((8a b c + 72a b )d + (8b c + 72a b c)d )x +--R + +--R 2 3 3 2 2 2 2 2 +--R (16a b c + 144a b)d + (32a b c + 288a b c)d +--R + +--R 3 3 3 2 +--R (16b c + 144a b c )d +--R * +--R 3 +--R x +--R + +--R 3 4 3 2 2 3 2 2 3 2 2 2 +--R (8a c + 72a )d + (40a b c + 360a b c)d + (40a b c + 360a b c )d +--R + +--R 3 4 3 3 +--R 8b c + 72a b c +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 4 2 2 3 +--R ((16a c + 144a c)d + (32a b c + 288a b c )d + 16a b c + 144a b c )x +--R + +--R 3 3 4 2 2 4 3 3 +--R (8a c + 72a c )d + 8a b c + 72a b c +--R / +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (9a b d - 36a b c d + 54a b c d - 36a b c d + 9b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 18a b d - 54a b c d + 36a b c d + 36a b c d - 54a b c d +--R + +--R 6 5 +--R 18b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (9a d - 81a b c d + 144a b c d - 81a b c d + 9b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (18a c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d + 18a b c )x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R (8a c + 72a )d + 8b c + 72a b c +--R (4) --------------------------------------------------- +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R 9a d - 36a b c d + 54a b c d - 36a b c d + 9b c +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=x/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-2/3*c/(d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2/3*(b*c+a*d)/_ + (d*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x))-8/3*(b*c+a*d)/_ + ((b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x))-16/3*d*(b*c+a*d)*_ + sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 16a b d - 16b c d )x + (- 24a b d - 48a b c d - 24b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 6a d - 42a b c d - 42a b c d - 6b c )x - 4a c d - 24a b c d - 4a b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 2 2 3 +--R (- 48a b c d - 48a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 72a b c d - 144a b c d - 72a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 +--R (- 18a c d - 126a b c d - 126a b c d - 18a b c )x - 12a c d +--R + +--R 3 3 2 2 4 +--R - 72a b c d - 12a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 2a b c - 18a b )d + (- 12a b c - 108a b c)d +--R + +--R 4 3 4 2 2 +--R (- 2b c - 18a b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 2 2 2 3 2 3 +--R (- 4a b c - 36a b)d + (- 28a b c - 252a b c)d +--R + +--R 3 3 2 3 2 2 4 4 4 3 +--R (- 28a b c - 252a b c )d + (- 4b c - 36a b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 2a c - 18a )d + (- 20a b c - 180a b c)d +--R + +--R 2 2 3 3 2 2 2 3 4 2 3 3 4 5 +--R (- 52a b c - 468a b c )d + (- 20a b c - 180a b c )d - 2b c +--R + +--R 4 4 +--R - 18a b c +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 4a c - 36a c)d + (- 28a b c - 252a b c )d +--R + +--R 2 2 4 3 2 3 3 5 2 3 4 +--R (- 28a b c - 252a b c )d - 4a b c - 36a b c +--R * +--R x +--R + +--R 4 3 5 2 2 3 4 4 3 2 2 5 3 2 4 +--R (- 2a c - 18a c )d + (- 12a b c - 108a b c )d - 2a b c - 18a b c +--R / +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 4 +--R (9a b c d - 36a b c d + 54a b c d - 36a b c d + 9a b c d )x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 18a b c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d +--R + +--R 6 6 +--R 18a b c d +--R * +--R 3 +--R x +--R + +--R 7 6 5 2 3 4 4 3 4 3 3 4 5 2 6 7 2 +--R (9a c d - 81a b c d + 144a b c d - 81a b c d + 9a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (18a c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d + 18a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (- 2a c - 18a )d + (- 12a b c - 108a b c)d - 2b c - 18a b c +--R (4) --------------------------------------------------------------- +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=1/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*d/((b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*_ + (c+d*x)^(3/2))+32/3*b*d^2*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 32b d x + (48a b d + 48b c d )x + (12a b d + 72a b c d + 12b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a d + 18a b c d + 18a b c d - 2b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 3 3 3 2 2 3 2 3 3 2 2 +--R 160a b c d x + (240a b c d + 240a b c d )x +--R + +--R 4 2 3 3 2 3 2 2 3 4 5 2 3 4 3 2 +--R (60a b c d + 360a b c d + 60a b c d)x - 10a c d + 90a b c d +--R + +--R 3 2 4 2 3 5 +--R 90a b c d - 10a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 2 4 2 5 2 3 2 3 3 4 +--R (- a b c - 25a b )d + (9a b c + 225a b c)d +--R + +--R 4 3 2 4 2 3 5 4 5 3 2 +--R (9a b c + 225a b c )d + (- b c - 25a b c )d +--R * +--R 4 +--R x +--R + +--R 4 5 5 3 2 2 4 2 4 +--R (- 2a b c - 50a b)d + (16a b c + 400a b c)d +--R + +--R 2 3 3 3 3 2 3 4 4 2 4 3 2 +--R (36a b c + 900a b c )d + (16a b c + 400a b c )d +--R + +--R 5 5 5 4 +--R (- 2b c - 50a b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 5 4 2 5 4 3 2 3 4 2 2 3 +--R (- a c - 25a )d + (5a b c + 125a b c)d + (44a b c + 1100a b c )d +--R + +--R 2 3 4 3 3 3 2 4 5 2 4 4 5 6 5 5 +--R (44a b c + 1100a b c )d + (5a b c + 125a b c )d - b c - 25a b c +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 2a c - 50a c)d + (16a b c + 400a b c )d +--R + +--R 3 2 4 4 2 3 2 2 3 5 3 3 4 4 6 2 4 5 +--R (36a b c + 900a b c )d + (16a b c + 400a b c )d - 2a b c - 50a b c +--R * +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 3 2 5 4 2 4 +--R (- a c - 25a c )d + (9a b c + 225a b c )d + (9a b c + 225a b c )d +--R + +--R 2 3 6 3 3 5 +--R - a b c - 25a b c +--R / +--R 6 2 2 6 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2 4 +--R (15a b c d - 60a b c d + 90a b c d - 60a b c d + 15a b c d )x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 +--R 30a b c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d +--R + +--R 2 6 7 +--R 30a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 6 6 2 4 4 5 3 5 3 4 4 6 2 2 6 8 2 +--R (15a c d - 135a b c d + 240a b c d - 135a b c d + 15a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R (30a c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d + 30a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 2 3 2 2 2 3 4 +--R (- a c - 25a )d + (9a b c + 225a b c)d + (9a b c + 225a b c )d - b c +--R + +--R 3 3 +--R - 25a b c +--R / +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=1/(x*(a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=2/3*b/(a*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-2*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+_ + 2*b*(b*c-3*a*d)/(a^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 2/3*d*(3*b^2*c^2-10*a*b*c*d-a^2*d^2)*sqrt(a+b*x)/(a^2*c*(b*c-a*d)^3*_ + (c+d*x)^(3/2))+2/3*d*(b*c+a*d)*(3*b^2*c^2-14*a*b*c*d+3*a^2*d^2)*_ + sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (- 6a b d + 24a b c d - 36a b c d + 24a b c d - 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 6a d + 18a b c d - 12a b c d - 12a b c d + 18a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (6a b d - 22a b c d - 22a b c d + 6b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b d - 36a b c d - 48a b c d - 36a b c d + 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 6a b c d - 48a b c d - 48a b c d - 6a b c d + 6b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R 8a c d - 24a b c d - 24a b c d + 8a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 2 5 6 2 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=1/(x^2*(a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-1/3*b*(5*b*c-3*a*d)/(a^2*c*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1)/_ + (a*c*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5*(b*c+a*d)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_ + b*(5*b^2*c^2-10*a*b*c*d+a^2*d^2)/(a^3*c*(b*c-a*d)^2*(c+d*x)^(3/2)*_ + sqrt(a+b*x))-1/3*d*(15*b^3*c^3-35*a*b^2*c^2*d+9*a^2*b*c*d^2-_ + 5*a^3*d^3)*sqrt(a+b*x)/(a^3*c^2*(b*c-a*d)^3*(c+d*x)^(3/2))-_ + 1/3*d*(15*b^4*c^4-40*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+_ + 15*a^4*d^4)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 6 5 +--R 15b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 15a d - 30a b c d - 15a b c d + 60a b c d - 15a b c d +--R + +--R 5 5 6 6 +--R - 30a b c d + 15b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 15a c d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 5 6 +--R 15a b c +--R * +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (- 15a b d + 40a b c d - 18a b c d + 40a b c d - 15b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 30a b d + 60a b c d + 18a b c d + 18a b c d + 60a b c d +--R + +--R 6 5 +--R - 30b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (- 15a d + 87a b c d - 48a b c d + 87a b c d - 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 20a c d + 48a b c d - 12a b c d - 12a b c d + 48a b c d +--R + +--R 5 6 +--R - 20a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R - 3a c d + 12a b c d - 18a b c d + 12a b c d - 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 3 5 7 3 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 2 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R (3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=1/(x^3*(a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 7 2 2 6 2 2 2 2 5 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 4 2 2 3 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=1/12*b*(35*b^2*c^2-6*a*b*c*d-21*a^2*d^2)/(a^3*c^2*(b*c-a*d)*_ + (a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1/2)/(a*c*x^2*(a+b*x)^(3/2)*_ + (c+d*x)^(3/2))+7/4*(b*c+a*d)/(a^2*c^2*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))-_ + 5/4*(7*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_ + (sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))+1/4*b*(35*b^3*c^3-_ + 55*a*b^2*c^2*d-3*a^2*b*c*d^2+7*a^3*d^3)/(a^4*c^2*(b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(105*b^4*c^4-200*a*b^3*c^3*d+_ + 18*a^2*b^2*c^2*d^2+48*a^3*b*c*d^3-35*a^4*d^4)*sqrt(a+b*x)/_ + (a^4*c^3*(b*c-a*d)^3*(c+d*x)^(3/2))+1/12*d*(b*c+a*d)*(105*b^4*c^4-_ + 340*a*b^3*c^3*d+406*a^2*b^2*c^2*d^2-340*a^3*b*c*d^3+105*a^4*d^4)*_ + sqrt(a+b*x)/(a^4*c^4*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 105a b d + 270a b c d - 135a b c d - 60a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 135a b c d + 270a b c d - 105b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 105a d + 165a b c d + 135a b c d - 195a b c d - 195a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 135a b c d + 165a b c d - 105b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R - 105a c d + 270a b c d - 135a b c d - 60a b c d +--R + +--R 3 4 5 2 2 5 6 6 7 +--R - 135a b c d + 270a b c d - 105a b c +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 105a b d - 235a b c d + 66a b c d + 66a b c d - 235a b c d +--R + +--R 7 5 2 +--R 105b c d +--R * +--R 5 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 210a b d - 330a b c d - 186a b c d + 228a b c d - 186a b c d +--R + +--R 6 5 2 7 6 +--R - 330a b c d + 210b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 105a d + 45a b c d - 549a b c d + 207a b c d + 207a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 549a b c d + 45a b c d + 105b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R 140a c d - 276a b c d - 12a b c d + 168a b c d - 12a b c d +--R + +--R 2 5 6 6 7 +--R - 276a b c d + 140a b c +--R * +--R 2 +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 21a c d - 63a b c d + 42a b c d + 42a b c d - 63a b c d +--R + +--R 2 5 7 +--R 21a b c +--R * +--R x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 8 4 5 7 2 5 4 6 3 6 3 5 4 7 2 4 5 8 4 +--R (12a b c d - 48a b c d + 72a b c d - 48a b c d + 12a b c d)x +--R + +--R 9 4 5 8 5 4 7 2 6 3 6 3 7 2 5 4 8 +--R 12a c d - 36a b c d + 24a b c d + 24a b c d - 36a b c d +--R + +--R 4 5 9 +--R 12a b c +--R * +--R 3 +--R x +--R + +--R 9 5 4 8 6 3 7 2 7 2 6 3 8 5 4 9 2 +--R (12a c d - 48a b c d + 72a b c d - 48a b c d + 12a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=x^2*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (1) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=1/3*x^3*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R 3 +-------+ +--R x \|b x + a +--R (2) ------------- +--R +---------+ +--R 3\|- b x - a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 +---------+ +-------+ +--R x \|- b x - a \|b x + a +--R (3) - ------------------------ +--R 3b x + 3a +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=x*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R x\|b x + a +--R (1) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=1/2*x^2*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (2) ------------- +--R +---------+ +--R 2\|- b x - a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +---------+ +-------+ +--R x \|- b x - a \|b x + a +--R (3) - ------------------------ +--R 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=x*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R x\|b x + a +--R (2) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +-------+ +--R x\|- b x - a \|b x + a +--R (3) - ----------------------- +--R b x + a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=sqrt(a+b*x)/(x*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ------------- +--R +---------+ +--R x\|- b x - a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=log(x)*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R log(x)\|b x + a +--R (2) ---------------- +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=sqrt(a+b*x)/(x^2*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------- +--R 2 +---------+ +--R x \|- b x - a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=-sqrt(a+b*x)/(x*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (2) - ------------- +--R +---------+ +--R x\|- b x - a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=sqrt(a+b*x)/(x^3*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------- +--R 3 +---------+ +--R x \|- b x - a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-1/2*sqrt(a+b*x)/(x^2*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (2) - --------------- +--R 2 +---------+ +--R 2x \|- b x - a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 "Error detected within library code: Shouldn't happen" +a0:=integrate(t0,x) +--R +--R +--R 2 +---------+ +-------+ +--R (- x + 1)\|- b x - a \|b x + a +--R (3) -------------------------------- +--R 3 2 +--R 2b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R \|b x + a +--R (4) ------------- +--R +---------+ +--R 2\|- b x - a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=sqrt(a+b*x)/(x^m*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------- +--R m +---------+ +--R x \|- b x - a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=x^(1-m)*sqrt(a+b*x)/((1-m)*sqrt(-a-b*x)) +--R +--R +--R - m + 1 +-------+ +--R x \|b x + a +--R (2) - ------------------- +--R +---------+ +--R (m - 1)\|- b x - a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=x^2*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R 2 n +--R x (b x + a) +--R (1) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=1/3*x^3*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R 3 n +--R x (b x + a) +--R (2) ------------- +--R n +--R 3(- b x - a) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R x cos(n %pi) +--R (3) --------------------------- +--R 2 2 +--R 3sin(n %pi) + 3cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R 3 2 3 2 n 3 n +--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a) +--R (4) ---------------------------------------------------------------------- +--R 2 2 n +--R (3sin(n %pi) + 3cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 2 2 n +--R (- 3x sin(n %pi) - 3x cos(n %pi) )(- b x - a) +--R + +--R 3 2 3 2 n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 3 2 3 2 n n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R 2 n 2 +--R 3x cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (3sin(n %pi) + 3cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=x*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R n +--R x (b x + a) +--R (1) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=1/2*x^2*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R 2 n +--R x (b x + a) +--R (2) ------------- +--R n +--R 2(- b x - a) +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R x cos(n %pi) +--R (3) --------------------------- +--R 2 2 +--R 2sin(n %pi) + 2cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 2 2 n 2 n +--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a) +--R (4) ---------------------------------------------------------------------- +--R 2 2 n +--R (2sin(n %pi) + 2cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- 2x sin(n %pi) - 2x cos(n %pi) )(- b x - a) +--R + +--R 2 2 2 2 n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 2 2 n n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R 2x cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (2sin(n %pi) + 2cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(a+b*x)^n/(-a-b*x)^n +--R +--R +--R n +--R (b x + a) +--R (1) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=x*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R n +--R x (b x + a) +--R (2) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R x cos(n %pi) +--R (3) ------------------------- +--R 2 2 +--R sin(n %pi) + cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 n n +--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a) +--R (4) ---------------------------------------------------------------------- +--R 2 2 n +--R (sin(n %pi) + cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- sin(n %pi) - cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (sin(n %pi) + cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(a+b*x)^n/(x*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=(a+b*x)^n*log(x)/(-a-b*x)^n +--R +--R +--R n +--R log(x)(b x + a) +--R (2) ---------------- +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R cos(n %pi)log(x) +--R (3) ------------------------- +--R 2 2 +--R sin(n %pi) + cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n +--R (- log(x)sin(n %pi) - cos(n %pi) log(x))(b x + a) +--R + +--R n +--R cos(n %pi)log(x)(- b x - a) +--R / +--R 2 2 n +--R (sin(n %pi) + cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- sin(n %pi) - cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (- b n x log(x)sin(n %pi) - b n x cos(n %pi) log(x))(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n +--R (- b n x log(x)sin(n %pi) - b n x cos(n %pi) log(x))(- b x - a) +--R * +--R n - 1 +--R (b x + a) +--R + +--R n 2 +--R cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (x sin(n %pi) + x cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(a+b*x)^n/(x^2*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R 2 n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-(a+b*x)^n/(x*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (2) - -------------- +--R n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R cos(n %pi) +--R (3) - ----------------------------- +--R 2 2 +--R x sin(n %pi) + x cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 n n +--R (sin(n %pi) + cos(n %pi) )(b x + a) - cos(n %pi)(- b x - a) +--R (4) -------------------------------------------------------------- +--R 2 2 n +--R (x sin(n %pi) + x cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- sin(n %pi) - cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R cos(n %pi)((- b x - a) ) +--R / +--R 2 2 2 2 n 2 +--R (x sin(n %pi) + x cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(a+b*x)^n/(x^3*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R 3 n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1/2*(a+b*x)^n/(x^2*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (2) - --------------- +--R 2 n +--R 2x (- b x - a) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R cos(n %pi) +--R (3) - ------------------------------- +--R 2 2 2 2 +--R 2x sin(n %pi) + 2x cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 n n +--R (sin(n %pi) + cos(n %pi) )(b x + a) - cos(n %pi)(- b x - a) +--R (4) -------------------------------------------------------------- +--R 2 2 2 2 n +--R (2x sin(n %pi) + 2x cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- 2sin(n %pi) - 2cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R 2cos(n %pi)((- b x - a) ) +--R / +--R 3 2 3 2 n 2 +--R (2x sin(n %pi) + 2x cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(a+b*x)^n/(x^m*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R n m +--R (- b x - a) x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=x^(1-m)*(a+b*x)^n/((1-m)*(-a-b*x)^n) +--R +--R +--R - m + 1 n +--R x (b x + a) +--R (2) - ------------------- +--R n +--R (m - 1)(- b x - a) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R x cos(n %pi) +--R (3) - --------------------------------------------------- +--R 2 2 m log(x) +--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )%e +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 - m + 1 n m log(x) +--R (sin(n %pi) + cos(n %pi) )x (b x + a) %e +--R + +--R n +--R - x cos(n %pi)(- b x - a) +--R / +--R 2 2 n m log(x) +--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )(- b x - a) %e +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n - 1 - m + 1 +--R (b n sin(n %pi) + b n cos(n %pi) )(- b x - a) x +--R + +--R 2 2 n - m +--R ((- m + 1)sin(n %pi) + (- m + 1)cos(n %pi) )(- b x - a) x +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n - m + 1 n - 1 +--R (b n sin(n %pi) + b n cos(n %pi) )(- b x - a) x (b x + a) +--R * +--R m log(x) +--R %e +--R + +--R n 2 +--R (m - 1)cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 m log(x) +--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )((- b x - a) ) %e +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=x^3*sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R 3 +-----+ +--R x \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+11/2*asin(x)-6*sqrt(1+x)/sqrt(1-x)-_ + 3*sqrt(1-x)*sqrt(1+x)-1/2*x*sqrt(1-x^2),11/2*asin(x)+2/3*x^3*_ + sqrt(1+x)/(1-x)^(3/2)-13/3*x^2*sqrt(1+x)/sqrt(1-x)-13/3*sqrt(1-x)*_ + sqrt(1+x)-1/6*(26+33*x)*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R [ +--R 2 +-----+ +--R (18x - 74x + 52)\|x + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R ((- 3x + 3x)\|- x + 1 + (33x - 33)asin(x))\|- x + 1 +--R / +--R +-------+ +--R (6x - 6)\|- x + 1 +--R , +--R 3 2 +-----+ +-------+ +--R (3x + 12x - 71x + 52)\|x + 1 + (33x - 33)asin(x)\|- x + 1 +--R -------------------------------------------------------------] +--R +-------+ +--R (6x - 6)\|- x + 1 +--R Type: Tuple(Expression(Integer)) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=x^2*sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R x \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x)-4*sqrt(1+x)/sqrt(1-x)-_ + sqrt(1-x)*sqrt(1+x),1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x)-_ + 2*(1+x)^(3/2)/sqrt(1-x)-3*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R [----------------------------------------------------, +--R +-------+ +--R (3x - 3)\|- x + 1 +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R ----------------------------------------------------] +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Tuple(Expression(Integer)) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=x*sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x)-2*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-----+ +-------+ +--R (- 7x + 5)\|x + 1 + (3x - 3)asin(x)\|- x + 1 +--R (2) ---------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 500 +--m0:=a0-r0 +--E 234 + +--S 235 of 500 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 500 +t0:=sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (2) ------------------ +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-----+ 2 +--R (8x + 8)\|- x + 1 \|x + 1 - 17x + 34x - 17 +--R (3) -------------------------------------------- +--R 2 +--R 24x - 48x + 24 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 17 +--R (4) - -- +--R 24 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=sqrt(1+x)/(-1+x)^(5/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) --------------------- +--R 2 +-----+ +--R (x - 2x + 1)\|x - 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-1/3*(1+x)^(3/2)/(-1+x)^(3/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (2) ----------------- +--R +-----+ +--R (3x - 3)\|x - 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ 2 +--R (- 3x - 3)\|x - 1 \|x + 1 + 4x - 8x + 4 +--R (3) ----------------------------------------- +--R 2 +--R 9x - 18x + 9 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - +--R 9 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=sqrt(1+x)/((1-x)^(5/2)*x) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ------------------------ +--R 3 2 +-------+ +--R (x - 2x + x)\|- x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=-2*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/(1-x)^(3/2)+_ + 5/3*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-------+ +--R +-------+ \|- x + 1 +-----+ +--R (- 6x + 6)\|- x + 1 atanh(----------) + (5x - 7)\|x + 1 +--R +-----+ +--R \|x + 1 +--R (2) -------------------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-----+ +--R 2 - \|- x + 1 \|x + 1 - 1 +--R (- 3x + 6x - 3)log(------------------------) +--R x +--R + +--R +-------+ +-----+ 2 +--R (- 5x + 7)\|- x + 1 \|x + 1 - 3x + 6x - 3 +--R / +--R 2 +--R 3x - 6x + 3 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-------+ +-----+ +-------+ +--R - \|- x + 1 \|x + 1 - 1 \|- x + 1 +--R (4) - log(------------------------) + 2atanh(----------) - 1 +--R x +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=sqrt(1+x)/((1-x)^(5/2)*x^2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ------------------------- +--R 4 3 2 +-------+ +--R (x - 2x + x )\|- x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=-6*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x)+_ + 3*sqrt(1+x)/(x*sqrt(1-x))-14/3*sqrt(1-x)*sqrt(1+x)/x +--R +--R +--R +-------+ +--R 2 +-------+ \|- x + 1 2 +-----+ +--R (- 18x + 18x)\|- x + 1 atanh(----------) + (14x - 19x + 3)\|x + 1 +--R +-----+ +--R \|x + 1 +--R (2) -------------------------------------------------------------------- +--R 2 +-------+ +--R (3x - 3x)\|- x + 1 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-----+ +--R 3 2 \|- x + 1 \|x + 1 + 1 +--R (- 144x + 288x - 144x)log(----------------------) +--R x +--R + +--R 2 +-------+ +-----+ 3 2 +--R (- 224x + 304x - 48)\|- x + 1 \|x + 1 + 273x - 546x + 273x +--R / +--R 3 2 +--R 48x - 96x + 48x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-------+ +-----+ +-------+ +--R \|- x + 1 \|x + 1 + 1 \|- x + 1 +--R - 48log(----------------------) + 96atanh(----------) + 91 +--R x +-----+ +--R \|x + 1 +--R (4) ---------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=sqrt(1+x)/((1-x)^(5/2)*x^3) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ------------------------- +--R 5 4 3 +-------+ +--R (x - 2x + x )\|- x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-11*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x^2)+_ + 13/3*sqrt(1+x)/(x^2*sqrt(1-x))-11/2*sqrt(1-x)*sqrt(1+x)/x^2-_ + 26/3*sqrt(1-x)*sqrt(1+x)/x +--R +--R +--R (2) +--R +-------+ +--R 3 2 +-------+ \|- x + 1 3 2 +-----+ +--R (- 66x + 66x )\|- x + 1 atanh(----------) + (52x - 71x + 12x + 3)\|x + 1 +--R +-----+ +--R \|x + 1 +--R ---------------------------------------------------------------------------- +--R 3 2 +-------+ +--R (6x - 6x )\|- x + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-----+ +--R 4 3 2 - \|- x + 1 \|x + 1 - 1 +--R (- 528x + 1056x - 528x )log(------------------------) +--R x +--R + +--R 3 2 +-------+ +-----+ 4 3 2 +--R (- 832x + 1136x - 192x - 48)\|- x + 1 \|x + 1 - 159x + 318x - 159x +--R / +--R 4 3 2 +--R 96x - 192x + 96x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-------+ +-----+ +-------+ +--R - \|- x + 1 \|x + 1 - 1 \|- x + 1 +--R - 176log(------------------------) + 352atanh(----------) - 53 +--R x +-----+ +--R \|x + 1 +--R (4) -------------------------------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=x^2/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 2 +--R x +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=1/2*acosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 + acosh(x) +--R (2) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) + x\|x - 1 \|x + 1 +--R (3) ----------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) - acosh(x) +--R (4) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (5) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=x/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R x +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (2) \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R (3) \|x - 1 \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=1/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=acosh(x) +--R +--R +--R (2) acosh(x) +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R (3) - log(- \|x - 1 \|x + 1 + x) +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R (4) - log(- \|x - 1 \|x + 1 + x) - acosh(x) +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (5) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=1/(x*sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=2*atan(sqrt(-1+x)/sqrt(1+x)) +--R +--R +--R +-----+ +--R \|x - 1 +--R (2) 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 +--R (3) atan(-----------------------) +--R +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 \|x - 1 +--R (4) atan(-----------------------) - 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 \|x + 1 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=1/(x^2*sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 1 +--R (1) ------------------ +--R 2 +-----+ +-----+ +--R x \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=sqrt(-1+x)*sqrt(1+x)/x +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (2) ---------------- +--R x +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 + x +--R (3) -------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) 1 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=x^2*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R 2 +-----+ +-----+ +--R (1) x \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-1/8*acosh(x)-1/8*x*sqrt(-1+x)*sqrt(1+x)+1/4*x^3*sqrt(-1+x)*_ + sqrt(1+x),1/4*(-1+x)^(3/2)*x*(1+x)^(3/2)-1/8*acosh(x)+_ + 1/8*(-1+x)^(3/2)*sqrt(1+x)+1/8*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R (2) +--R 3 +-----+ +-----+ 3 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) (2x - x)\|x - 1 \|x + 1 - acosh(x) +--R [------------------------------------,------------------------------------] +--R 8 8 +--R Type: Tuple(Expression(Integer)) +--E 287 + +--S 288 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ 3 +-----+ +-----+ +--R - log(- \|x - 1 \|x + 1 - x) + (2x - x)\|x - 1 \|x + 1 +--R (3) --------------------------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R - log(- \|x - 1 \|x + 1 - x) + acosh(x) +--R (4) ---------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (5) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 8\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (1) x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=1/3*(-1+x)^(3/2)*(1+x)^(3/2) +--R +--R +--R 2 +-----+ +-----+ +--R (x - 1)\|x - 1 \|x + 1 +--R (2) ------------------------ +--R 3 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R 2 +-----+ +-----+ +--R (x - 1)\|x - 1 \|x + 1 +--R (3) ------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (1) \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=-1/2*acosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x),_ + -1/2*acosh(x)+1/2*(-1+x)^(3/2)*sqrt(1+x)+1/2*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R x\|x - 1 \|x + 1 - acosh(x) x\|x - 1 \|x + 1 - acosh(x) +--R (2) [----------------------------,----------------------------] +--R 2 2 +--R Type: Tuple(Expression(Integer)) +--E 297 + +--S 298 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (- 4x\|x - 1 \|x + 1 - 4x + 2)log(\|x + 1 + \|x - 1 ) +--R + +--R 3 +-----+ +-----+ 4 2 +--R (2x - x)\|x - 1 \|x + 1 + 2x - 2x +--R / +--R +-----+ +-----+ 2 +--R 4x\|x - 1 \|x + 1 + 4x - 2 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R - 2log(\|x + 1 + \|x - 1 ) + acosh(x) +--R (4) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (5) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=sqrt(-1+x)*sqrt(1+x)/x +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) ---------------- +--R x +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=-2*atan(sqrt(-1+x)/sqrt(1+x))+sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +--R \|x - 1 +-----+ +-----+ +--R (2) - 2atan(--------) + \|x - 1 \|x + 1 +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 +-----+ +-----+ +--R (3) - atan(-----------------------) + \|x - 1 \|x + 1 +--R +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 \|x - 1 +--R (4) - atan(-----------------------) + 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 \|x + 1 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=sqrt(-1+x)*sqrt(1+x)/x^2 +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) ---------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=acosh(x)-sqrt(-1+x)*sqrt(1+x)/x +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x acosh(x) +--R (2) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - x log(\|x - 1 \|x + 1 - x) - \|x - 1 \|x + 1 + x +--R (3) ---------------------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R (4) - log(\|x - 1 \|x + 1 - x) - acosh(x) + 1 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (5) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/(sqrt(1+2*x)*sqrt(3+2*x)) +--R +--R +--R 1 +--R (1) ------------------ +--R +------+ +------+ +--R \|2x + 1 \|2x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=asinh(sqrt(1+2*x)/sqrt(2)) +--R +--R +--R +------+ +--R \|2x + 1 +--R (2) asinh(---------) +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R log(- \|2x + 1 \|2x + 3 + 2x + 2) +--R (3) - ---------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +------+ +--R +------+ +------+ \|2x + 1 +--R - log(- \|2x + 1 \|2x + 3 + 2x + 2) - 2asinh(---------) +--R +-+ +--R \|2 +--R (4) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/(x*sqrt(-2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +------+ +------+ +--R x\|3x - 2 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=atan(sqrt(3/2)*sqrt(-2+3*x)/sqrt(3+5*x))*sqrt(2/3) +--R +--R +--R +-+ +------+ +--R +-+ \|3 \|3x - 2 +--R \|2 atan(-------------) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (2) ----------------------- +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (- 337x - 4044)\|2 \|3 +--R \|2 \|3 atan(-------------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 + 456x + 5472 +--R (3) --------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (- 337x - 4044)\|2 \|3 +--R \|2 atan(-------------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 + 456x + 5472 +--R + +--R +-+ +------+ +--R +-+ \|3 \|3x - 2 +--R - 2\|2 atan(-------------) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R / +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((-1+x)^(3/2)*x*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 3 +-----+ +-----+ +--R (x - x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=-2*atan(sqrt(-1+x)/sqrt(1+x))+(-1)/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R - 2\|x - 1 \|x + 1 atan(--------) - 1 +--R +-----+ +--R \|x + 1 +--R (2) ------------------------------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+ +-----+ +--R 2 16\|x - 1 \|x + 1 - 63 +-----+ +-----+ 2 +--R (- 12x + 12)atan(-----------------------) - 12\|x - 1 \|x + 1 - 7x + 7 +--R +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 +--R ------------------------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 \|x - 1 +--R - 12atan(-----------------------) + 24atan(--------) - 7 +--R +-----+ +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 \|x + 1 +--R (4) -------------------------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=x*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-------+ +-----+ +--R (1) x\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1/3*(1-x)^(3/2)*(1+x)^(3/2) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (2) -------------------------- +--R 3 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (3) -------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=x^3*(2+3*x)^(3/2)*(1+4*x)^(1/2) +--R +--R +--R 4 3 +------+ +------+ +--R (1) (3x + 2x )\|3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=22357/6635520*(2+3*x)^(3/2)*(1+4*x)^(3/2)+1/92160*(8-403*x)*_ + (2+3*x)^(3/2)*(1+4*x)^(3/2)-1/960*x^2*(2+3*x)^(3/2)*(1+4*x)^(3/2)+_ + 1/24*x^3*(2+3*x)^(3/2)*(1+4*x)^(3/2)+1067875/84934656*_ + asinh(sqrt(3/5)*sqrt(1+4*x))/sqrt(3)-42715/5308416*(2+3*x)^(3/2)*_ + sqrt(1+4*x)+213575/42467328*sqrt(2+3*x)*sqrt(1+4*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|3 \|4x + 1 +--R 5339375asinh(-------------) +--R +-+ +--R \|5 +--R + +--R 5 4 3 2 +--R 212336640x + 189333504x + 8239104x - 3699456x + 2179184x +--R + +--R - 1763226 +--R * +--R +-+ +------+ +------+ +--R \|3 \|3x + 2 \|4x + 1 +--R / +--R +-+ +--R 424673280\|3 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/(sqrt(-1+a+b*x)*sqrt(1+a+b*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=2*asinh(sqrt(-1+a+b*x)/sqrt(2))/b +--R +--R +--R +-----------+ +--R \|b x + a - 1 +--R 2asinh(--------------) +--R +-+ +--R \|2 +--R (2) ---------------------- +--R b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=x^2*(1+x)^(1/4)/(1-x)^(1/4) +--R +--R +--R 2 4+-----+ +--R x \|x + 1 +--R (1) ---------- +--R 4+-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-3/8*(1-x)^(3/4)*(1+x)^(1/4)-1/12*(1-x)^(3/4)*(1+x)^(5/4)-_ + 1/3*(1-x)^(3/4)*x*(1+x)^(5/4)+3/8*atan(1-(1-x)^(1/4)*sqrt(2)/_ + (1+x)^(1/4))/sqrt(2)-3/8*atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/_ + sqrt(2)-3/16*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/_ + sqrt(1+x))/sqrt(2)+3/16*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+_ + sqrt(1-x)/sqrt(1+x))/sqrt(2) +--R +--R +--R (2) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R 9log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - 9log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+ +--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1 +--R - 18atan(-------------------------) + 18atan(-------------------------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 2 +-+4+-------+3 4+-----+ +--R (- 16x - 20x - 22)\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 48\|2 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=x*(1+x)^(1/4)/(1-x)^(1/4) +--R +--R +--R 4+-----+ +--R x\|x + 1 +--R (1) ---------- +--R 4+-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-1/4*(1-x)^(3/4)*(1+x)^(1/4)-1/2*(1-x)^(3/4)*(1+x)^(5/4)+_ + 1/4*atan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_ + 1/4*atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_ + 1/8*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/_ + sqrt(2)+1/8*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+_ + sqrt(1-x)/sqrt(1+x))/sqrt(2) +--R +--R +--R (2) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+ +--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1 +--R - 2atan(-------------------------) + 2atan(-------------------------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+4+-------+3 4+-----+ +--R (- 4x - 6)\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1+x)^(1/4)/(1-x)^(1/4) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ---------- +--R 4+-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-(1-x)^(3/4)*(1+x)^(1/4)+atan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/_ + sqrt(2)-atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_ + 1/2*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/_ + sqrt(2)+1/2*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/_ + sqrt(1+x))/sqrt(2) +--R +--R +--R (2) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+ +--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1 +--R - 2atan(-------------------------) + 2atan(-------------------------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+4+-------+3 4+-----+ +--R - 2\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ----------- +--R 4+-------+ +--R x\|- x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-2*atan((1+x)^(1/4)/(1-x)^(1/4))-2*atanh((1+x)^(1/4)/(1-x)^(1/4))-_ + log(1-(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4)+sqrt(1+x)/sqrt(1-x))/_ + sqrt(2)+log(1+(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4)+sqrt(1+x)/_ + sqrt(1-x))/sqrt(2)-atan(1-(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4))*_ + sqrt(2)+atan(1+(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4))*sqrt(2) +--R +--R +--R (2) +--R +-+ +-------+4+-----+ 4+-------+ +-----+ +-------+4+-------+ +--R \|2 \|- x + 1 \|x + 1 + \|- x + 1 \|x + 1 + \|- x + 1 \|- x + 1 +--R log(------------------------------------------------------------------) +--R +-------+4+-------+ +--R \|- x + 1 \|- x + 1 +--R + +--R - +--R log +--R +-+ +-------+4+-----+ 4+-------+ +-----+ +--R - \|2 \|- x + 1 \|x + 1 + \|- x + 1 \|x + 1 +--R + +--R +-------+4+-------+ +--R \|- x + 1 \|- x + 1 +--R / +--R +-------+4+-------+ +--R \|- x + 1 \|- x + 1 +--R + +--R 4+-----+ +-+4+-----+ 4+-------+ +--R +-+ \|x + 1 \|2 \|x + 1 + \|- x + 1 +--R - 2\|2 atanh(----------) + 2atan(-------------------------) +--R 4+-------+ 4+-------+ +--R \|- x + 1 \|- x + 1 +--R + +--R +-+4+-----+ 4+-------+ 4+-----+ +--R \|2 \|x + 1 - \|- x + 1 +-+ \|x + 1 +--R 2atan(-------------------------) - 2\|2 atan(----------) +--R 4+-------+ 4+-------+ +--R \|- x + 1 \|- x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^2) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ------------ +--R 2 4+-------+ +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-(1-x)^(3/4)*(1+x)^(1/4)/x+atan((1-x)^(1/4)/(1+x)^(1/4))-_ + atanh((1-x)^(1/4)/(1+x)^(1/4)) +--R +--R +--R 4+-------+ 4+-------+ +--R \|- x + 1 \|- x + 1 4+-------+3 4+-----+ +--R - x atanh(----------) + x atan(----------) - \|- x + 1 \|x + 1 +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R (2) ---------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^3) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ------------ +--R 3 4+-------+ +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-1/2*(1-x)^(3/4)*(1+x)^(1/4)/x^2-3/4*(1-x)^(3/4)*(1+x)^(1/4)/x+_ + 1/4*atan((1-x)^(1/4)/(1+x)^(1/4))-1/4*atanh((1-x)^(1/4)/(1+x)^(1/4)) +--R +--R +--R (2) +--R 4+-------+ 4+-------+ +--R 2 \|- x + 1 2 \|- x + 1 4+-------+3 4+-----+ +--R - x atanh(----------) + x atan(----------) + (- 3x - 2)\|- x + 1 \|x + 1 +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R -------------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^4) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ------------ +--R 4 4+-------+ +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-1/3*(1-x)^(3/4)*(1+x)^(1/4)/x^3-5/12*(1-x)^(3/4)*(1+x)^(1/4)/x^2-_ + 11/24*(1-x)^(3/4)*(1+x)^(1/4)/x+3/8*atan((1-x)^(1/4)/(1+x)^(1/4))-_ + 3/8*atanh((1-x)^(1/4)/(1+x)^(1/4)) +--R +--R +--R (2) +--R 4+-------+ 4+-------+ +--R 3 \|- x + 1 3 \|- x + 1 +--R - 9x atanh(----------) + 9x atan(----------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 2 4+-------+3 4+-----+ +--R (- 11x - 10x - 8)\|- x + 1 \|x + 1 +--R / +--R 3 +--R 24x +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=x^3*(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 3 4+-------+ +--R x \|b x + a +--R (1) ------------ +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-1/1536*(585*b^3*c^3-63*a*b^2*c^2*d-61*a^2*b*c*d^2-77*a^3*d^3)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^4)-1/384*(10*a*c-_ + 117*b*c^2/d+11*a^2*d/b)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)-_ + 1/48*(13*b*c-a*d)*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+_ + 1/4*x^3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/d+1/1024*(b*c-a*d)*_ + (195*b^3*c^3+135*a*b^2*c^2*d+105*a^2*b*c*d^2+77*a^3*d^3)*_ + atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*_ + d^(17/4))+1/1024*(b*c-a*d)*(195*b^3*c^3+135*a*b^2*c^2*d+_ + 105*a^2*b*c*d^2+77*a^3*d^3)*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(17/4)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 231a d - 84a b c d - 90a b c d - 180a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 231a d - 84a b c d - 90a b c d - 180a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 768b d x + (64a b d - 832b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 88a b d - 80a b c d + 936b c d)x + 154a d + 122a b c d +--R + +--R 2 2 3 3 +--R 126a b c d - 1170b c +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 4 4+-+3 4+-+ +--R 3072b d \|b \|d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=x^2*(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 2 4+-------+ +--R x \|b x + a +--R (1) ------------ +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=1/32*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (b^2*d^3)-1/24*(9*b*c+7*a*d)*(a+b*x)^(5/4)*(c+d*x)^(3/4)/_ + (b^2*d^2)+1/3*x*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)-1/64*_ + (b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*atan(d^(1/4)*_ + (a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4))-_ + 1/64*(b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*_ + atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (21a d + 9a b c d + 15a b c d - 45b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (21a d + 9a b c d + 15a b c d - 45b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 4+-+3 +--R (64b d x + (8a b d - 72b c d)x - 14a d - 12a b c d + 90b c )\|b +--R * +--R 4+-+4+-------+4+-------+3 +--R \|d \|b x + a \|d x + c +--R / +--R 2 3 4+-+3 4+-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=x*(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 4+-------+ +--R x\|b x + a +--R (1) ----------- +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1/8*(5*b*c+3*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+_ + 1/2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)+1/16*(b*c-a*d)*_ + (5*b*c+3*a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(7/4)*d^(9/4))+1/16*(b*c-a*d)*(5*b*c+3*a*d)*_ + atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- 3a d - 2a b c d + 5b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- 3a d - 2a b c d + 5b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R (8b d x + 2a d - 10b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 4+-+3 4+-+ +--R 16b d \|b \|d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ---------- +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=(a+b*x)^(1/4)*(c+d*x)^(3/4)/d-1/2*(b*c-a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4))-1/2*(b*c-a*d)*_ + atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R (a d - b c)atanh(--------------) + (a d - b c)atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R 2\|b \|d \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2d \|b \|d +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(a+b*x)^(1/4)/(x*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ----------- +--R 4+-------+ +--R x\|d x + c +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-2*a^(1/4)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+_ + 2*b^(1/4)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4)-_ + 2*a^(1/4)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+_ + 2*b^(1/4)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R 4+-+4+-+ \|d \|b x + a 4+-+4+-+ \|c \|b x + a +--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|a \|d x + c +--R + +--R 4+-+4+-------+ 4+-+4+-------+ +--R 4+-+4+-+ \|d \|b x + a 4+-+4+-+ \|c \|b x + a +--R 2\|b \|c atan(--------------) - 2\|a \|d atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|a \|d x + c +--R / +--R 4+-+4+-+ +--R \|c \|d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(a+b*x)^(1/4)/(x^2*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 2 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x)-1/2*(b*c-a*d)*_ + atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(5/4))-_ + 1/2*(b*c-a*d)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(3/4)*c^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|c \|b x + a \|c \|b x + a +--R (a d - b c)x atanh(--------------) + (a d - b c)x atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|a \|d x + c \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R - 2\|a \|c \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2c x \|a \|c +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(a+b*x)^(1/4)/(x^3*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 3 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^2)-1/8*(b*c-5*a*d)*(a+b*x)^(1/4)*_ + (c+d*x)^(3/4)/(a*c^2*x)+1/16*(b*c-a*d)*(3*b*c+5*a*d)*_ + atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(7/4)*c^(9/4))+1/16*(b*c-a*d)*(3*b*c+5*a*d)*atanh(c^(1/4)*_ + (a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d + 2a b c d + 3b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d + 2a b c d + 3b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R ((10a d - 2b c)x - 8a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 4+-+3 4+-+ +--R 16a c x \|a \|c +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(a+b*x)^(1/4)/(x^4*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 4 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^3)-1/24*(b*c-9*a*d)*(a+b*x)^(1/4)*_ + (c+d*x)^(3/4)/(a*c^2*x^2)+1/96*(7*b*c-15*a*d)*(b*c+3*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^3*x)-1/64*(b*c-a*d)*_ + (7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*atan(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4))-1/64*(b*c-a*d)*_ + (7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d - 15a b c d - 9a b c d - 21b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d - 15a b c d - 9a b c d - 21b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 90a d + 12a b c d + 14b c )x + (72a c d - 8a b c )x - 64a c ) +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|a \|c \|b x + a \|d x + c +--R / +--R 2 3 3 4+-+3 4+-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(a+b*x)^(1/4)/(x^5*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 5 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-1/4*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^4)-1/48*(b*c-13*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c^2*x^3)+1/384*(11*b^2*c^2+_ + 10*a*b*c*d-117*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (a^2*c^3*x^2)-1/1536*(77*b^3*c^3+61*a*b^2*c^2*d+63*a^2*b*c*d^2-_ + 585*a^3*d^3)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^3*c^4*x)+_ + 1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+135*a^2*b*c*d^2+_ + 195*a^3*d^3)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(15/4)*c^(17/4))+1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+_ + 135*a^2*b*c*d^2+195*a^3*d^3)*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(17/4)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 585a d + 180a b c d + 90a b c d + 84a b c d + 231b c )x +--R * +--R 4+-+4+-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 585a d + 180a b c d + 90a b c d + 84a b c d + 231b c )x +--R * +--R 4+-+4+-------+ +--R \|c \|b x + a +--R atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (1170a d - 126a b c d - 122a b c d - 154b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 +--R (- 936a c d + 80a b c d + 88a b c )x + (832a c d - 64a b c )x +--R + +--R 3 3 +--R - 768a c +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 4 4 4+-+3 4+-+ +--R 3072a c x \|a \|c +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=x^4/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-1/1536*(585*b^3*c^3+657*a*b^2*c^2*d+803*a^2*b*c*d^2+1155*a^3*d^3)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^4*d^4)+1/384*(117*b^2*c^2+_ + 134*a*b*c*d+165*a^2*d^2)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^3)-_ + 1/48*(13*b*c+15*a*d)*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+_ + 1/4*x^3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/1024*(195*b^4*c^4+_ + 180*a*b^3*c^3*d+210*a^2*b^2*c^2*d^2+308*a^3*b*c*d^3+1155*a^4*d^4)*_ + atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(19/4)*d^(17/4))+_ + 1/1024*(195*b^4*c^4+180*a*b^3*c^3*d+210*a^2*b^2*c^2*d^2+_ + 308*a^3*b*c*d^3+1155*a^4*d^4)*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(19/4)*d^(17/4)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (3465a d + 924a b c d + 630a b c d + 540a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (3465a d + 924a b c d + 630a b c d + 540a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 768b d x + (- 960a b d - 832b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (1320a b d + 1072a b c d + 936b c d)x - 2310a d - 1606a b c d +--R + +--R 2 2 3 3 +--R - 1314a b c d - 1170b c +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 4 4+-+3 4+-+ +--R 3072b d \|b \|d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=x^3/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=1/96*(45*b^2*c^2+54*a*b*c*d+77*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (b^3*d^3)-1/24*(9*b*c+11*a*d)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (b^2*d^2)+1/3*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-_ + 1/64*(15*b^3*c^3+15*a*b^2*c^2*d+21*a^2*b*c*d^2+77*a^3*d^3)*_ + atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(15/4)*d^(13/4))-1/64*(15*b^3*c^3+15*a*b^2*c^2*d+_ + 21*a^2*b*c*d^2+77*a^3*d^3)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(15/4)*d^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 231a d - 63a b c d - 45a b c d - 45b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 231a d - 63a b c d - 45a b c d - 45b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (64b d x + (- 88a b d - 72b c d)x + 154a d + 108a b c d + 90b c ) +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 3 4+-+3 4+-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=x^2/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=-1/8*(5*b*c+7*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+_ + 1/2*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/16*(5*b^2*c^2+_ + 6*a*b*c*d+21*a^2*d^2)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(11/4)*d^(9/4))+1/16*(5*b^2*c^2+6*a*b*c*d+_ + 21*a^2*d^2)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(11/4)*d^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (21a d + 6a b c d + 5b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (21a d + 6a b c d + 5b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R (8b d x - 14a d - 10b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 2 4+-+3 4+-+ +--R 16b d \|b \|d +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=x/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-1/2*(b*c+3*a*d)*atan(d^(1/4)*_ + (a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(5/4))-_ + 1/2*(b*c+3*a*d)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(7/4)*d^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R (- 3a d - b c)atanh(--------------) + (- 3a d - b c)atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R 2\|b \|d \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2b d \|b \|d +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=1/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=2*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(3/4)*d^(1/4))+2*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(1/4)) +--R +--R +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R 2atanh(--------------) + 2atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R (2) ---------------------------------------------- +--R 4+-+3 4+-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=1/(x*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-2*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(3/4)*c^(1/4))-2*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(1/4)) +--R +--R +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|c \|b x + a \|c \|b x + a +--R - 2atanh(--------------) - 2atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|a \|d x + c \|a \|d x + c +--R (2) ------------------------------------------------ +--R 4+-+3 4+-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=1/(x^2*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x)+1/2*(3*b*c+a*d)*_ + atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(5/4))+_ + 1/2*(3*b*c+a*d)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(7/4)*c^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|c \|b x + a \|c \|b x + a +--R (a d + 3b c)x atanh(--------------) + (a d + 3b c)x atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|a \|d x + c \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R - 2\|a \|c \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2a c x \|a \|c +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=1/(x^3*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^2)+1/8*(7*b*c+5*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x)-1/16*(21*b^2*c^2+_ + 6*a*b*c*d+5*a^2*d^2)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*_ + (c+d*x)^(1/4)))/(a^(11/4)*c^(9/4))-1/16*(21*b^2*c^2+6*a*b*c*d+_ + 5*a^2*d^2)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(11/4)*c^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d - 6a b c d - 21b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d - 6a b c d - 21b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R ((10a d + 14b c)x - 8a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 2 4+-+3 4+-+ +--R 16a c x \|a \|c +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=1/(x^4*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^3)+1/24*(11*b*c+9*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x^2)-_ + 1/96*(77*b^2*c^2+54*a*b*c*d+45*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (a^3*c^3*x)+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+15*a^2*b*c*d^2+_ + 15*a^3*d^3)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(15/4)*c^(13/4))+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+_ + 15*a^2*b*c*d^2+15*a^3*d^3)*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d + 45a b c d + 63a b c d + 231b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d + 45a b c d + 63a b c d + 231b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 90a d - 108a b c d - 154b c )x + (72a c d + 88a b c )x - 64a c ) +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 3 3 4+-+3 4+-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=1/((1-a*x)^(1/4)*(1+b*x)^(3/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4+---------+4+-------+3 +--R \|- a x + 1 \|b x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-log(-a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+sqrt(a)+_ + sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + log(a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+_ + sqrt(a)+sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*_ + sqrt(2))+atan(1-b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*_ + (1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4))-atan(1+b^(1/4)*_ + (1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*(1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4)) +--R +--R +--R (2) +--R log +--R +-+ +-------+ +---------+ +-+ 4+-------+ +--R (\|a \|b x + 1 + \|- a x + 1 \|b )\|b x + 1 +--R + +--R +-+4+---------+4+-+4+-+ +-------+ +--R \|2 \|- a x + 1 \|a \|b \|b x + 1 +--R / +--R +-------+4+-------+ +--R \|b x + 1 \|b x + 1 +--R + +--R - +--R log +--R +-+ +-------+ +---------+ +-+ 4+-------+ +--R (\|a \|b x + 1 + \|- a x + 1 \|b )\|b x + 1 +--R + +--R +-+4+---------+4+-+4+-+ +-------+ +--R - \|2 \|- a x + 1 \|a \|b \|b x + 1 +--R / +--R +-------+4+-------+ +--R \|b x + 1 \|b x + 1 +--R + +--R 4+-+4+-------+ +-+4+---------+4+-+ +--R \|a \|b x + 1 + \|2 \|- a x + 1 \|b +--R - 2atan(-------------------------------------) +--R 4+-+4+-------+ +--R \|a \|b x + 1 +--R + +--R 4+-+4+-------+ +-+4+---------+4+-+ +--R \|a \|b x + 1 - \|2 \|- a x + 1 \|b +--R 2atan(-------------------------------------) +--R 4+-+4+-------+ +--R \|a \|b x + 1 +--R / +--R +-+4+-+4+-+3 +--R \|2 \|a \|b +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=1/((1-a*x)^(1/4)*(1+a*x)^(3/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4+---------+4+-------+3 +--R \|- a x + 1 \|a x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-log(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/sqrt(1+a*x))/_ + (a*sqrt(2))+log(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/_ + sqrt(1+a*x))/(a*sqrt(2))+atan(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*_ + sqrt(2)/a-atan(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*sqrt(2)/a +--R +--R +--R (2) +--R +-------+ +---------+ 4+-------+ +-+4+---------+ +-------+ +--R (\|a x + 1 + \|- a x + 1 )\|a x + 1 + \|2 \|- a x + 1 \|a x + 1 +--R log(------------------------------------------------------------------) +--R +-------+4+-------+ +--R \|a x + 1 \|a x + 1 +--R + +--R +-------+ +---------+ 4+-------+ +-+4+---------+ +-------+ +--R (\|a x + 1 + \|- a x + 1 )\|a x + 1 - \|2 \|- a x + 1 \|a x + 1 +--R - log(------------------------------------------------------------------) +--R +-------+4+-------+ +--R \|a x + 1 \|a x + 1 +--R + +--R 4+-------+ +-+4+---------+ +--R \|a x + 1 + \|2 \|- a x + 1 +--R - 2atan(-----------------------------) +--R 4+-------+ +--R \|a x + 1 +--R + +--R 4+-------+ +-+4+---------+ +--R \|a x + 1 - \|2 \|- a x + 1 +--R 2atan(-----------------------------) +--R 4+-------+ +--R \|a x + 1 +--R / +--R +-+ +--R a\|2 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-%i*x)^(1/6*%i)*x^3/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 3 6 +--R x (- %i x + 1) +--R (1) ---------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 476 + +--S 477 of 500 +--r0:=1/4*x^4*AppellF1(4,-1/6*%i,1/6*%i,5,%i*x,-%i*x),(-18/37+3/37*%i)*_ +-- 2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*AppellF1(1+1/6*%i,1/6*%i,_ +-- -3,2+1/6*%i,1/2*(1-%i*x),1-%i*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-%i*x)^(1/6*%i)*x^2/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 2 6 +--R x (- %i x + 1) +--R (1) ---------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 481 + +--S 482 of 500 +--r0:=-1/18*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)+_ +-- 1/3*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)*x+_ +-- (-17/333+34/111*%i)*2^(1/6*%i)*(1+%i*x)^(1-1/6*%i)*_ +-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x)) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-%i*x)^(1/6*%i)*x/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 6 +--R x (- %i x + 1) +--R (1) ---------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 486 + +--S 487 of 500 +--r0:=1/2*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)+_ +-- (-1/37+6/37*%i)*2^(1/6*%i)*(1+%i*x)^(1-1/6*%i)*_ +-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x)) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-%i*x)^(1/6*%i)/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 491 + +--S 492 of 500 +--r0:=(3/37-18/37*%i)*2^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)*_ +-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x)) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 6 +--R x (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 496 + +--S 497 of 500 +--r0:-(-18/37+3/37*%i)*2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)* +-- AppellF1(1+1/6*%i,1/6*%i,1,2+1/6*%i,1/2*(1-%i*x),1-%i*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + diff --git a/src/axiom-website/CATS/rich3c.input.pdf b/src/axiom-website/CATS/rich3c.input.pdf new file mode 100644 index 0000000..5182c84 Binary files /dev/null and b/src/axiom-website/CATS/rich3c.input.pdf differ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index e5fec42..5cd6db4 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4250,6 +4250,8 @@ src/axiom-website/CATS/rich1b statistics update src/axiom-website/CATS/rich2, rich3a 20130726.01.tpd.patch src/axiom-website/CATS/rich3b +20130727.01.tpd.patch +src/axiom-website/CATS/rich3c diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index d6bfd68..49f31b2 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -433,7 +433,7 @@ These long-running tests have been split into a different group so we can run them in parallel. <>= NEWRICHTESTS = rich1a.regress rich1b.regress rich2.regress \ - rich3a.regress rich3b.regress + rich3a.regress rich3b.regress rich3c.regress RICHTESTS= \ richalgebraic000-099.regress \ @@ -789,6 +789,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/ribbons.input ${OUT}/ribbonsnew.input \ ${OUT}/rich1a.input ${OUT}/rich1b.input \ ${OUT}/rich2.input ${OUT}/rich3a.input ${OUT}/rich3b.input \ + ${OUT}/rich3c.input \ ${OUT}/rk4draw.input \ ${OUT}/r20abugs.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ @@ -875,6 +876,7 @@ FILES2=${OUT}/arith.input ${OUT}/bugs.input \ NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input \ ${OUT}/rich2.input ${OUT}/rich3a.input ${OUT}/rich3b.input \ + ${OUT}/rich3c.input RICHINPUT= \ ${OUT}/richalgebraic000-099.input \ @@ -1196,6 +1198,7 @@ DOCFILES= \ ${DOC}/rich1a.input.dvi ${DOC}/rich1b.input.dvi \ ${DOC}/rich2.input.dvi \ ${DOC}/rich3a.input.dvi ${DOC}/rich3b.input.dvi \ + ${DOC}/rich3c.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ diff --git a/src/input/rich3c.input.pamphlet b/src/input/rich3c.input.pamphlet new file mode 100644 index 0000000..88bdf31 --- /dev/null +++ b/src/input/rich3c.input.pamphlet @@ -0,0 +1,6734 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file +\item 100 supplied "optimal results" +\item 25 matching answers +\item 12 answers that differ from the optimal results +\item 58 cases that Axiom failed to integrate +\item 5 that contain expressions Axiom does not recognize +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3c.output +)spool rich3c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=x^5/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 5 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=5/4*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+1/2*a*(b*c-5*a*d)*x^3/(b^2*d*_ + (b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+1/2*x^4/(b*d*(c+d*x)^(3/2)*_ + sqrt(a+b*x))+1/6*c*(7*b^2*c^2-6*a*b*c*d+15*a^2*d^2)*x^2*_ + sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^2*(c+d*x)^(3/2))+1/6*_ + c*(4*a*c*(7*b^2*c^2-6*a*b*c*d+15*a^2*d^2)+(35*b^3*c^3-_ + 33*a*b^2*c^2*d-15*a^2*b*c*d^2+45*a^3*d^3)*x)*sqrt(a+b*x)/_ + (b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x))-1/12*(3*b*c-a*d)*_ + (35*b^3*c^3-33*a*b^2*c^2*d-15*a^2*b*c*d^2+45*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d +--R + +--R 5 5 +--R - 105b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R 45a c d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (- 15a b d + 24a b c d + 18a b c d - 48a b c d + 21b c d )x +--R + +--R 5 6 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (- 45a d + 66a b c d + 12a b c d - 237a b c d + 140b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 90a c d + 45a b c d + 84a b c d - 222a b c d - 50a b c d +--R + +--R 5 6 +--R 105b c +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 45a c d + 30a b c d + 36a b c d - 190a b c d + 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 3 8 2 4 7 5 2 6 6 3 5 3 3 7 +--R (12a b d - 36a b c d + 36a b c d - 12b c d )x + 12a b c d +--R + +--R 2 4 2 6 5 3 5 6 4 4 +--R - 36a b c d + 36a b c d - 12b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=x^4/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 4 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-(5*b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(5/2)*d^(7/2))+a*(b*c-3*a*d)*x^2/(b^2*d*(b*c-a*d)*(c+d*x)^(3/2)*_ + sqrt(a+b*x))+x^3/(b*d*(c+d*x)^(3/2)*sqrt(a+b*x))+1/3*c*_ + (4*a*c*(b*c-3*a*d)+(b*c-a*d)*(5*b*c+3*a*d)*x)*sqrt(a+b*x)/_ + (b^2*d^2*(b*c-a*d)^2*(c+d*x)^(3/2))+1/3*c*(15*b^3*c^3-_ + 35*a*b^2*c^2*d+25*a^2*b*c*d^2-21*a^3*d^3)*sqrt(a+b*x)/_ + (b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c d)x - 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 18a b c d - 36a b c d + 15b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (9a d - 3a b c d - 9a b c d + 39a b c d - 20b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (18a c d - 15a b c d + 33a b c d + 11a b c d - 15b c )x + 9a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 9a b c d + 31a b c d - 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 2 7 2 3 6 4 2 5 5 3 4 3 2 6 2 3 2 5 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 4 3 4 5 4 3 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=x^3/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 3 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))-_ + 2*x^3/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+8/3*c*x^2*sqrt(a+b*x)/_ + ((b*c-a*d)^2*(c+d*x)^(3/2))+4/3*c*(8*a*c+(b*c+3*a*d)*x)*_ + sqrt(a+b*x)/(d*(b*c-a*d)^3*sqrt(c+d*x))-2/3*(3*b*c-a*d)*_ + (b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 18a b c d + 18a b c d - 6b c d)x + 6a c d - 18a b c d +--R + +--R 2 3 3 4 +--R 18a b c d - 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 4 2 2 2 3 3 2 +--R (- 6a d - 18a b c d + 8b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 +--R (- 12a c d - 18a b c d - 8a b c d + 6b c )x - 6a c d - 16a b c d +--R + +--R 2 4 +--R 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 6 2 2 5 3 2 4 4 3 3 3 5 2 2 2 4 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 3 3 3 4 4 2 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=x^2/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-2*a^2/(b^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*(b^2*c^2+3*a^2*d^2)*_ + sqrt(a+b*x)/(b^2*d*(b*c-a*d)^2*(c+d*x)^(3/2))+_ + 2/3*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^3*_ + sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (6a d + 12a b c d - 2b c )x + (24a c d + 8a b c )x + 16a c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R ((30a d + 60a b c d - 10b c )x + (120a c d + 40a b c )x + 80a c ) +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 3 2 3 2 2 2 2 +--R (8a b c + 200a b)d x + ((8a c + 200a )d + (16a b c + 400a b c)d)x +--R + +--R 2 2 3 3 2 2 2 3 3 2 +--R ((16a c + 400a c)d + 8a b c + 200a b c )x + 8a c + 200a c +--R / +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (15a b d - 45a b c d + 45a b c d - 15b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 15a b c d - 45a b c d + 75a b c d - 30b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (30a c d - 75a b c d + 45a b c d + 15a b c d - 15b c )x + 15a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 45a b c d + 45a b c d - 15a b c +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 +--R 8a c + 200a +--R (4) ---------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R 15a d - 45a b c d + 45a b c d - 15b c +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=x/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=2*a/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b*c+3*a*d)*_ + sqrt(a+b*x)/(b*(b*c-a*d)^2*(c+d*x)^(3/2))+4/3*(b*c+3*a*d)*_ + sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (- 12a b d - 4b c d)x + (- 6a d - 20a b c d - 6b c )x - 4a c d +--R + +--R 2 +--R - 12a b c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 3 +--R (- 36a b c d - 12b c d)x + (- 18a c d - 60a b c d - 18b c )x +--R + +--R 2 2 3 +--R - 12a c d - 36a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 3 2 2 2 2 3 +--R ((- 2a b c - 18a b)d + (- 6b c - 54a b c)d )x +--R + +--R 2 3 3 2 2 2 +--R (- 2a c - 18a )d + (- 10a b c - 90a b c)d +--R + +--R 2 3 2 2 +--R (- 12b c - 108a b c )d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 2 4 2 3 +--R ((- 4a c - 36a c)d + (- 14a b c - 126a b c )d - 6b c - 54a b c )x +--R + +--R 2 3 3 2 4 2 3 +--R (- 2a c - 18a c )d - 6a b c - 54a b c +--R / +--R 3 5 2 2 2 4 3 3 3 4 4 2 3 +--R (9a b c d - 27a b c d + 27a b c d - 9b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 2 +--R (9a c d - 9a b c d - 27a b c d + 45a b c d - 18b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4 3 3 +--R (18a c d - 45a b c d + 27a b c d + 9a b c d - 9b c )x + 9a c d +--R + +--R 3 4 2 2 2 5 3 6 +--R - 27a b c d + 27a b c d - 9a b c +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R (- 2a c - 18a )d - 6b c - 54a b c +--R (4) ---------------------------------------- +--R 3 3 2 2 2 2 3 3 4 +--R 9a c d - 27a b c d + 27a b c d - 9b c +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=1/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=(-2)/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-_ + 8/3*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(3/2))-_ + 16/3*b*d*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R 16b d x + (8a b d + 24b c d)x - 2a d + 12a b c d + 6b c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 3 3 2 2 2 3 +--R 64a b c d x + (32a b c d + 96a b c d)x - 8a c d + 48a b c d +--R + +--R 2 4 +--R 24a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 3 4 2 2 2 2 3 3 3 3 2 2 3 +--R ((- a b c - 16a b)d + (6a b c + 96a b c)d + (3b c + 48a b c )d )x +--R + +--R 3 4 4 2 2 3 3 2 3 2 2 2 2 +--R (- a c - 16a )d + (4a b c + 64a b c)d + (15a b c + 240a b c )d +--R + +--R 3 4 3 3 +--R (6b c + 96a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 2a c - 32a c)d + (11a b c + 176a b c )d +--R + +--R 2 4 2 2 3 3 5 3 4 +--R (12a b c + 192a b c )d + 3b c + 48a b c +--R * +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 2 5 2 2 4 +--R (- a c - 16a c )d + (6a b c + 96a b c )d + 3a b c + 48a b c +--R / +--R 4 2 5 3 2 3 4 2 3 4 3 4 5 2 3 +--R (12a b c d - 36a b c d + 36a b c d - 12a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (12a c d - 12a b c d - 36a b c d + 60a b c d - 24a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (24a c d - 60a b c d + 36a b c d + 12a b c d - 12a b c )x + 12a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R - 36a b c d + 36a b c d - 12a b c +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (- a c - 16a )d + (6a b c + 96a b c)d + 3b c + 48a b c +--R (4) ---------------------------------------------------------- +--R 4 2 3 3 3 2 2 2 4 3 5 +--R 12a c d - 36a b c d + 36a b c d - 12a b c +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=1/(x*(a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 2 4 2 3 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))+_ + 2*b/(a*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 2/3*d*(3*b*c+a*d)*sqrt(a+b*x)/(a*c*(b*c-a*d)^2*(c+d*x)^(3/2))+_ + 2/3*d*(3*b*c-a*d)*(b*c+3*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c d)x - 6a c d + 18a b c d +--R + +--R 2 3 3 4 +--R - 18a b c d + 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 2 3 3 2 2 2 +--R (6a b d - 16a b c d - 6b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 8a b c d - 18a b c d - 12b c d)x + 8a c d - 18a b c d +--R + +--R 3 4 +--R - 6b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x + 3a c d - 9a b c d +--R + +--R 2 2 5 3 6 +--R 9a b c d - 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=1/(x^2*(a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=(3*b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (a^(5/2)*c^(7/2))-b*(3*b*c-a*d)/(a^2*c*(b*c-a*d)*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+(-1)/(a*c*x*(c+d*x)^(3/2)*sqrt(a+b*x))-_ + 1/3*d*(9*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)/(a^2*_ + c^2*(b*c-a*d)^2*(c+d*x)^(3/2))-1/3*d*(9*b^3*c^3-9*a*_ + b^2*c^2*d+31*a^2*b*c*d^2-15*a^3*d^3)*sqrt(a+b*x)/(a^2*_ + c^3*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (15a c d - 36a b c d + 18a b c d + 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 15a b d + 31a b c d - 9a b c d + 9b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 15a d + 11a b c d + 33a b c d - 15a b c d + 18b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 20a c d + 39a b c d - 9a b c d - 3a b c d + 9b c )x - 3a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=1/(x^3*(a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 6 2 5 2 4 2 3 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=-5/4*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_ + (sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))+1/4*b*(15*b^2*c^2-_ + 7*a^2*d^2)/(a^3*c^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + (-1/2)/(a*c*x^2*(c+d*x)^(3/2)*sqrt(a+b*x))+1/4*(5*b*c+7*a*d)/_ + (a^2*c^2*x*(c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(45*b^3*c^3-_ + 15*a*b^2*c^2*d-33*a^2*b*c*d^2+35*a^3*d^3)*sqrt(a+b*x)/_ + (a^3*c^3*(b*c-a*d)^2*(c+d*x)^(3/2))+1/12*d*(45*b^4*c^4-_ + 30*a*b^3*c^3*d-36*a^2*b^2*c^2*d^2+190*a^3*b*c*d^3-105*a^4*d^4)*_ + sqrt(a+b*x)/(a^3*c^4*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R - 105a d + 225a b c d - 90a b c d - 30a b c d - 45a b c d +--R + +--R 5 5 +--R 45b c d +--R * +--R 3 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 105a c d + 225a b c d - 90a b c d - 30a b c d - 45a b c d +--R + +--R 5 6 +--R 45b c +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 4 +--R (105a b d - 190a b c d + 36a b c d + 30a b c d - 45b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 105a d - 50a b c d - 222a b c d + 84a b c d + 45a b c d +--R + +--R 5 5 +--R - 90b c d +--R * +--R 3 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 6 2 +--R (140a c d - 237a b c d + 12a b c d + 66a b c d - 45b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R (21a c d - 48a b c d + 18a b c d + 24a b c d - 15a b c )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 4 4 5 5 3 4 2 6 2 3 3 7 3 +--R (12a c d - 36a b c d + 36a b c d - 12a b c d)x +--R + +--R 6 5 3 5 6 2 4 2 7 3 3 8 2 +--R (12a c d - 36a b c d + 36a b c d - 12a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 500 +--m0:=a0-r0 +--E 44 + +--S 45 of 500 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 500 +t0:=x^4*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 6 5 2 4 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=-2/3*x^4*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+1/128*(b*c-a*d)*_ + (3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*_ + b*c*d^3+3003*a^4*d^4)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(c+d*x)))/(b^(15/2)*d^(5/2))-2/3*(8*b*c-13*a*d)*_ + x^3*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))+1/192*_ + (3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*_ + b*c*d^3+3003*a^4*d^4)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^6*d^2*_ + (b*c-a*d))-1/240*(15*b^3*c^3+125*a*b^2*c^2*d-2343*a^2*_ + b*c*d^2+3003*a^3*d^3)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^5*d^2*_ + (b*c-a*d))+1/120*(15*b^2*c^2-902*a*b*c*d+1287*a^2*d^2)*_ + x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))+1/15*(93*_ + b*c-143*a*d)*x^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))+_ + 1/128*(3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-_ + 2772*a^3*b*c*d^3+3003*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^7*d^2) +--R +--R +--R (2) +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R - 45045a b d + 86625a b c d - 47250a b c d + 5250a b c d +--R + +--R 5 4 6 5 +--R 375a b c d + 45b c +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 +--R - 45045a d + 86625a b c d - 47250a b c d + 5250a b c d +--R + +--R 2 4 4 5 5 +--R 375a b c d + 45a b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 6 4 6 5 4 6 3 5 +--R 384b d x + (- 624a b d + 1008b c d )x +--R + +--R 2 4 4 5 3 6 2 2 4 +--R (1144a b d - 1888a b c d + 744b c d )x +--R + +--R 3 3 4 2 4 3 5 2 2 6 3 3 +--R (- 2574a b d + 4378a b c d - 1834a b c d + 30b c d)x +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (9009a b d - 16038a b c d + 7404a b c d - 330a b c d - 45b c )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 +--R 60060a b d - 97482a b c d + 38646a b c d - 750a b c d +--R + +--R 5 4 +--R - 90a b c +--R * +--R x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 45045a d - 71610a b c d + 27384a b c d - 390a b c d - 45a b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R / +--R 8 2 7 2 +-+ +-+ +-------+ +--R (1920b d x + 1920a b d )\|b \|d \|b x + a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 500 +--m0:=a0-r0 +--E 49 + +--S 50 of 500 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 500 +t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-2/3*x^3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))-5/64*(b*c-a*d)*_ + (b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(13/2)*d^(3/2))-_ + 2/3*(6*b*c-11*a*d)*x^2*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-_ + 5/96*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_ + (c+d*x)^(3/2)*sqrt(a+b*x)/(b^5*d*(b*c-a*d))+1/24*(5*b^2*c^2-_ + 156*a*b*c*d+231*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))+_ + 1/12*(59*b*c-99*a*d)*x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))-_ + 5/64*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^6*d) +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (3465a b d - 6300a b c d + 3150a b c d - 300a b c d - 15b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3465a d - 6300a b c d + 3150a b c d - 300a b c d - 15a b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 3 5 4 3 5 2 4 +--R 48b d x + (- 88a b d + 136b c d )x +--R + +--R 2 3 3 4 2 5 2 3 +--R (198a b d - 316a b c d + 118b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 693a b d + 1161a b c d - 483a b c d + 15b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (- 4620a b d + 7014a b c d - 2472a b c d + 30a b c )x - 3465a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 5145a b c d - 1743a b c d + 15a b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R / +--R 7 6 +-+ +-+ +-------+ +--R (192b d x + 192a b d)\|b \|d \|b x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 500 +--m0:=a0-r0 +--E 54 + +--S 55 of 500 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 500 +t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=-2/3*a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+_ + 5/8*(b*c-a*d)*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*sqrt(d))+_ + 4/3*a*(3*b*c-5*a*d)*(c+d*x)^(7/2)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))+_ + 5/12*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/_ + (b^4*(b*c-a*d))+1/3*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(5/2)*_ + sqrt(a+b*x)/(b^3*(b*c-a*d)^2)+5/8*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 315a b d + 525a b c d - 225a b c d + 15b c )x - 315a d +--R + +--R 3 2 2 2 2 3 3 +--R 525a b c d - 225a b c d + 15a b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 2 4 3 2 4 3 +--R 8b d x + (- 18a b d + 26b c d)x +--R + +--R 2 2 2 3 4 2 2 +--R (63a b d - 96a b c d + 33b c )x +--R + +--R 3 2 2 2 3 2 4 2 3 +--R (420a b d - 574a b c d + 162a b c )x + 315a d - 420a b c d +--R + +--R 2 2 2 +--R 113a b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R / +--R 6 5 +-+ +-+ +-------+ +--R (24b x + 24a b )\|b \|d \|b x + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=x*(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +--R (d x + 2c d x + c x)\|d x + c +--R (1) -------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=2/3*a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x)^(3/2))+5/4*(3*b*c-7*a*d)*_ + (b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(d)/b^(9/2)-2/3*(3*b*c-7*a*d)*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*_ + sqrt(a+b*x))+5/6*d*(3*b*c-7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/_ + (b^3*(b*c-a*d))+5/4*d*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((105a b d - 150a b c d + 45b c )x + 105a d - 150a b c d + 45a b c ) +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R \|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 3 2 2 3 2 +--R 6b d x + (- 21a b d + 27b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 140a b d + 158a b c d - 24b c )x - 105a d + 115a b c d - 16a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 5 4 +-+ +-------+ +--R (12b x + 12a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-2/3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+5*d^(3/2)*(b*c-a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-_ + 10/3*d*(c+d*x)^(3/2)/(b^2*sqrt(a+b*x))+5*d^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 +-+ +-------+ +--R ((- 15a b d + 15b c d)x - 15a d + 15a b c d)\|d \|b x + a +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (3b d x + (20a b d - 14b c d)x + 15a d - 10a b c d - 2b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(c+d*x)^(5/2)/(x*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) -------------------------------- +--R 2 3 2 2 +-------+ +--R (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=2/3*(c+d*x)^(5/2)/(a*(a+b*x)^(3/2))-2*c^(5/2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(5/2)+2*d^(5/2)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)+_ + 2/3*(3*b*c+2*a*d)*(c+d*x)^(3/2)/(a^2*b*sqrt(a+b*x))-_ + 2*d*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*b^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 3 2 +-+ +-+ +-------+ \|d \|b x + a +--R (6a b d x + 6a d )\|a \|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 3 2 2 2 +-+ +-+ +-------+ \|c \|b x + a +--R (- 6b c x - 6a b c )\|b \|c \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 3 2 3 2 2 2 2 +-+ +-+ +--R ((- 8a b d + 2a b c d + 6b c )x - 6a d - 2a b c d + 8a b c )\|a \|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 3 3 2 +-+ +-+ +-------+ +--R (3a b x + 3a b )\|a \|b \|b x + a +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-5/3*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x)^(3/2))-(c+d*x)^(5/2)/_ + (a*x*(a+b*x)^(3/2))+5*c^(3/2)*(b*c-a*d)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(7/2)-5*c*(b*c-a*d)*_ + sqrt(c+d*x)/(a^3*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 +-+ +-------+ +--R ((- 15a b c d + 15b c )x + (- 15a c d + 15a b c )x)\|c \|b x + a +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R ((2a d + 10a b c d - 15b c )x + (14a c d - 20a b c )x - 3a c )\|a +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 2 4 +-+ +-------+ +--R (3a b x + 3a x)\|a \|b x + a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 5 4 2 3 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=1/4*(7*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x)^(3/2))-1/2*(c+d*x)^(5/2)/_ + (a*x^2*(a+b*x)^(3/2))-5/4*(7*b*c-3*a*d)*(b*c-a*d)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(9/2)+_ + 1/12*(35*b*c-29*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*(a+b*x)^(3/2))+_ + 1/12*(105*b^2*c^2-115*a*b*c*d+16*a^2*d^2)*sqrt(c+d*x)/(a^4*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 +--R (- 45a b d + 150a b c d - 105b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 45a d + 150a b c d - 105a b c )x +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|c \|b x + a +--R \|c \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 3 2 3 +--R (16a b d - 115a b c d + 105b c )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (24a d - 158a b c d + 140a b c )x + (- 27a c d + 21a b c )x - 6a c +--R * +--R +-+ +-------+ +--R \|a \|d x + c +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x + 12a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 6 5 2 4 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=1/12*(9*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x)^(3/2))-_ + 1/3*(c+d*x)^(5/2)/(a*x^3*(a+b*x)^(3/2))+5/8*(b*c-a*d)*_ + (21*b^2*c^2-14*a*b*c*d+a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_ + (sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*sqrt(c))-7/24*b*(15*b*c-7*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/(a^4*(a+b*x)^(3/2))-1/8*(21*b*c-5*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/(a^3*x*(a+b*x)^(3/2))-_ + 1/24*b*(315*b^2*c^2-420*a*b*c*d+113*a^2*d^2)*sqrt(c+d*x)/(a^5*sqrt(a+b*x)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 225a b c d - 525a b c d + 315b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 225a b c d - 525a b c d + 315a b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 3 4 2 4 +--R (- 113a b d + 420a b c d - 315b c )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 162a b d + 574a b c d - 420a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 96a b c d - 63a b c )x + (- 26a c d + 18a b c )x - 8a c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +-+ +-------+ +--R (24a b x + 24a x )\|a \|c \|b x + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(c+d*x)^(5/2)/(x^5*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) --------------------------------- +--R 2 7 6 2 5 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=1/24*(11*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^3*(a+b*x)^(3/2))-_ + 1/4*(c+d*x)^(5/2)/(a*x^4*(a+b*x)^(3/2))-5/64*(b*c-a*d)*_ + (231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*_ + atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(13/2)*_ + c^(3/2))+1/64*b*(b*c-a*d)*(385*b^2*c^2-238*a*b*c*d+5*_ + a^2*d^2)*sqrt(c+d*x)/(a^5*c*(a+b*x)^(3/2))-1/32*(33*b*c-_ + 5*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*x^2*(a+b*x)^(3/2))+_ + 1/64*(b*c-a*d)*(231*b^2*c^2-156*a*b*c*d+5*a^2*d^2)*_ + sqrt(c+d*x)/(a^4*c*x*(a+b*x)^(3/2))+1/64*b*(1155*b^3*c^3-_ + 1715*a*b^2*c^2*d+581*a^2*b*c*d^2-5*a^3*d^3)*sqrt(c+d*x)/_ + (a^6*c*sqrt(a+b*x)) +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (15a b d + 300a b c d - 3150a b c d + 6300a b c d - 3465b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (15a d + 300a b c d - 3150a b c d + 6300a b c d - 3465a b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 15a b d + 1743a b c d - 5145a b c d + 3465b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 30a b d + 2472a b c d - 7014a b c d + 4620a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 15a d + 483a b c d - 1161a b c d + 693a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 +--R (- 118a c d + 316a b c d - 198a b c )x + (- 136a c d + 88a b c )x +--R + +--R 5 3 +--R - 48a c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R / +--R 6 5 7 4 +-+ +-+ +-------+ +--R (192a b c x + 192a c x )\|a \|c \|b x + a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=x^2/((a+b*x)^(5/2)*(c+d*x)^(1/2)) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (b x + 2a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))-_ + 2/3*a^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+_ + 4/3*a*(3*b*c-2*a*d)*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((6a b d - 12a b c d + 6b c )x + 6a d - 12a b c d + 6a b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 3 2 +-+ +-+ +-------+ +--R ((- 8a b d + 12a b c)x - 6a d + 10a b c)\|b \|d \|d x + c +--R / +--R 2 3 2 4 5 2 3 2 2 2 3 4 2 +-+ +-+ +--R ((3a b d - 6a b c d + 3b c )x + 3a b d - 6a b c d + 3a b c )\|b \|d +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=x^6/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=1/6*a*(3*b*c-7*a*d)*x^4/(b^2*d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_ + 1/2*x^5/(b*d*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5/4*(7*b^2*c^2+_ + 10*a*b*c*d+7*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))+1/6*a*_ + (3*b^2*c^2-62*a*b*c*d+35*a^2*d^2)*x^3/(b^3*d*(b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+1/6*c*(7*b^3*c^3-9*a*b^2*c^2*d+_ + 69*a^2*b*c*d^2-35*a^3*d^3)*x^2*sqrt(a+b*x)/(b^3*d^2*(b*c-a*d)^3*_ + (c+d*x)^(3/2))+1/6*c*(4*a*c*(7*b^3*c^3-9*a*b^2*c^2*d+_ + 69*a^2*b*c*d^2-35*a^3*d^3)+(35*b^4*c^4-48*a*b^3*c^3*d-_ + 18*a^2*b^2*c^2*d^2+200*a^3*b*c*d^3-105*a^4*d^4)*x)*_ + sqrt(a+b*x)/(b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x))-_ + 1/12*(3*b*c-a*d)*(35*b^4*c^4-48*a*b^3*c^3*d-18*a^2*b^2*c^2*d^2+_ + 200*a^3*b*c*d^3-105*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4*(b*c-a*d)^4) +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 105a b d - 270a b c d + 135a b c d + 60a b c d + 135a b c d +--R + +--R 6 5 2 7 6 +--R - 270a b c d + 105b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 105a d - 165a b c d - 135a b c d + 195a b c d + 195a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 135a b c d - 165a b c d + 105b c +--R * +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R 105a c d - 270a b c d + 135a b c d + 60a b c d + 135a b c d +--R + +--R 2 5 6 6 7 +--R - 270a b c d + 105a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 5 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 21a b d + 63a b c d - 42a b c d - 42a b c d + 63a b c d +--R + +--R 7 5 2 +--R - 21b c d +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 140a b d + 276a b c d + 12a b c d - 168a b c d + 12a b c d +--R + +--R 6 5 2 7 6 +--R 276a b c d - 140b c d +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 105a d - 45a b c d + 549a b c d - 207a b c d - 207a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 549a b c d - 45a b c d - 105b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R - 210a c d + 330a b c d + 186a b c d - 228a b c d +--R + +--R 3 4 5 2 2 5 6 6 7 +--R 186a b c d + 330a b c d - 210a b c +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R - 105a c d + 235a b c d - 66a b c d - 66a b c d + 235a b c d +--R + +--R 2 5 7 +--R - 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 9 4 5 2 +--R (12a b d - 48a b c d + 72a b c d - 48a b c d + 12b c d )x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 +--R 12a b d - 36a b c d + 24a b c d + 24a b c d - 36a b c d +--R + +--R 9 5 4 +--R 12b c d +--R * +--R x +--R + +--R 5 4 8 4 5 2 7 3 6 3 6 2 7 4 5 8 5 4 +--R 12a b c d - 48a b c d + 72a b c d - 48a b c d + 12a b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=x^5/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=1/3*a*(3*b*c-5*a*d)*x^3/(b^2*d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_ + x^4/(b*d*(a+b*x)^(3/2)*(c+d*x)^(3/2))-5*(b*c+a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+_ + a*(b^2*c^2-10*a*b*c*d+5*a^2*d^2)*x^2/(b^3*d*(b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+1/3*c*(4*a*c*(b^2*c^2-10*a*b*c*d+_ + 5*a^2*d^2)+5*(b*c-a*d)^2*(b*c+a*d)*x)*sqrt(a+b*x)/(b^3*d^2*_ + (b*c-a*d)^3*(c+d*x)^(3/2))+1/3*c*(15*b^4*c^4-44*a*b^3*c^3*d+_ + 62*a^2*b^2*c^2*d^2-100*a^3*b*c*d^3+35*a^4*d^4)*sqrt(a+b*x)/_ + (b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b d + 45a b c d - 30a b c d - 30a b c d + 45a b c d +--R + +--R 6 5 +--R - 15b c d +--R * +--R 2 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 15a d + 30a b c d + 15a b c d - 60a b c d + 15a b c d +--R + +--R 5 5 6 6 +--R 30a b c d - 15b c +--R * +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 15a c d + 45a b c d - 30a b c d - 30a b c d + 45a b c d +--R + +--R 5 6 +--R - 15a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 20a b d - 48a b c d + 12a b c d + 12a b c d - 48a b c d +--R + +--R 6 5 +--R 20b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (15a d - 87a b c d + 48a b c d - 87a b c d + 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 30a c d - 60a b c d - 18a b c d - 18a b c d - 60a b c d +--R + +--R 5 6 +--R 30a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 15a c d - 40a b c d + 18a b c d - 40a b c d + 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 +--R (3a b d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c d )x +--R + +--R 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 7 5 3 +--R 3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=x^4/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=-2/3*x^4/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_ + 4/3*(4*b*c-a*d)*x^3/(b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 4/3*c*(5*b*c-a*d)*x^2*sqrt(a+b*x)/(b*(b*c-a*d)^3*(c+d*x)^(3/2))+_ + 4/3*c*(4*a*c*(5*b*c-a*d)+(b^2*c^2+10*a*b*c*d-3*a^2*d^2)*x)*_ + sqrt(a+b*x)/(b*d*(b*c-a*d)^4*sqrt(c+d*x))-2/3*(3*b*c-a*d)*_ + (b^2*c^2+10*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_ + (b^2*d^2*(b*c-a*d)^4) +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 6a c d - 24a b c d + 36a b c d - 24a b c d + 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 8a b d + 24a b c d + 24a b c d - 8b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 6a d + 6a b c d + 48a b c d + 48a b c d + 6a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 12a c d + 36a b c d + 48a b c d + 36a b c d - 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 22a b c d + 22a b c d - 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 +--R (3a b d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c d )x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=x^3/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=-2/3*x^3/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-4*a^2*c/_ + (b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-4/3*c*_ + (b^2*c^2+3*a^2*d^2)*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^3*(c+d*x)^(3/2))+_ + 4/3*c*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^4*_ + sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (2a d - 18a b c d - 18a b c d + 2b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 12a c d - 72a b c d - 12a b c )x + (- 48a c d - 48a b c )x - 32a c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 +--R (2a d - 18a b c d - 18a b c d + 2b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 +--R (- 12a c d - 72a b c d - 12a b c )x + (- 48a c d - 48a b c )x +--R + +--R 3 3 +--R - 32a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 2 2 2 4 +--R (16a b c + 16a b c)d x +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R ((32a b c + 32a b c)d + (32a b c + 32a b c )d)x +--R + +--R 3 2 4 2 2 3 3 2 2 4 2 2 3 2 +--R ((16a c + 16a c)d + (64a b c + 64a b c )d + 16a b c + 16a b c )x +--R + +--R 3 3 4 2 2 4 3 3 3 4 4 3 +--R ((32a c + 32a c )d + 32a b c + 32a b c )x + 16a c + 16a c +--R / +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3 +--R (6a b d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6b c d)x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (3a d - 27a b c d + 48a b c d - 27a b c d + 3b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (6a c d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6a b c )x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R 16a c + 16a c +--R (4) --------------------------------------------------- +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3a d - 12a b c d + 18a b c d - 12a b c d + 3b c +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=x^2/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=-2/3*a^2/(b^2*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*a*c/_ + (b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b^2*c^2+_ + 6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b^2*(b*c-a*d)^3*(c+d*x)^(3/2))+_ + 4/3*(b^2*c^2+6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 +--R (4a b d + 24a b c d + 4b c d)x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d + 42a b c d + 42a b c d + 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 2 3 +--R (24a c d + 48a b c d + 24a b c )x + 16a c d + 16a b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 +--R (12a b d + 72a b c d + 12b c d)x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (18a d + 126a b c d + 126a b c d + 18b c )x +--R + +--R 3 2 2 2 2 3 3 2 2 3 +--R (72a c d + 144a b c d + 72a b c )x + 48a c d + 48a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 2 3 3 2 3 2 4 +--R ((8a b c + 72a b )d + (8b c + 72a b c)d )x +--R + +--R 2 3 3 2 2 2 2 2 +--R (16a b c + 144a b)d + (32a b c + 288a b c)d +--R + +--R 3 3 3 2 +--R (16b c + 144a b c )d +--R * +--R 3 +--R x +--R + +--R 3 4 3 2 2 3 2 2 3 2 2 2 +--R (8a c + 72a )d + (40a b c + 360a b c)d + (40a b c + 360a b c )d +--R + +--R 3 4 3 3 +--R 8b c + 72a b c +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 4 2 2 3 +--R ((16a c + 144a c)d + (32a b c + 288a b c )d + 16a b c + 144a b c )x +--R + +--R 3 3 4 2 2 4 3 3 +--R (8a c + 72a c )d + 8a b c + 72a b c +--R / +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (9a b d - 36a b c d + 54a b c d - 36a b c d + 9b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 18a b d - 54a b c d + 36a b c d + 36a b c d - 54a b c d +--R + +--R 6 5 +--R 18b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (9a d - 81a b c d + 144a b c d - 81a b c d + 9b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (18a c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d + 18a b c )x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R (8a c + 72a )d + 8b c + 72a b c +--R (4) --------------------------------------------------- +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R 9a d - 36a b c d + 54a b c d - 36a b c d + 9b c +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=x/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R x +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-2/3*c/(d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2/3*(b*c+a*d)/_ + (d*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x))-8/3*(b*c+a*d)/_ + ((b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x))-16/3*d*(b*c+a*d)*_ + sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 16a b d - 16b c d )x + (- 24a b d - 48a b c d - 24b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 6a d - 42a b c d - 42a b c d - 6b c )x - 4a c d - 24a b c d - 4a b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 2 2 3 +--R (- 48a b c d - 48a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 72a b c d - 144a b c d - 72a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 +--R (- 18a c d - 126a b c d - 126a b c d - 18a b c )x - 12a c d +--R + +--R 3 3 2 2 4 +--R - 72a b c d - 12a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 2a b c - 18a b )d + (- 12a b c - 108a b c)d +--R + +--R 4 3 4 2 2 +--R (- 2b c - 18a b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 2 2 2 3 2 3 +--R (- 4a b c - 36a b)d + (- 28a b c - 252a b c)d +--R + +--R 3 3 2 3 2 2 4 4 4 3 +--R (- 28a b c - 252a b c )d + (- 4b c - 36a b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 2a c - 18a )d + (- 20a b c - 180a b c)d +--R + +--R 2 2 3 3 2 2 2 3 4 2 3 3 4 5 +--R (- 52a b c - 468a b c )d + (- 20a b c - 180a b c )d - 2b c +--R + +--R 4 4 +--R - 18a b c +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 4a c - 36a c)d + (- 28a b c - 252a b c )d +--R + +--R 2 2 4 3 2 3 3 5 2 3 4 +--R (- 28a b c - 252a b c )d - 4a b c - 36a b c +--R * +--R x +--R + +--R 4 3 5 2 2 3 4 4 3 2 2 5 3 2 4 +--R (- 2a c - 18a c )d + (- 12a b c - 108a b c )d - 2a b c - 18a b c +--R / +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 4 +--R (9a b c d - 36a b c d + 54a b c d - 36a b c d + 9a b c d )x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 18a b c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d +--R + +--R 6 6 +--R 18a b c d +--R * +--R 3 +--R x +--R + +--R 7 6 5 2 3 4 4 3 4 3 3 4 5 2 6 7 2 +--R (9a c d - 81a b c d + 144a b c d - 81a b c d + 9a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (18a c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d + 18a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (- 2a c - 18a )d + (- 12a b c - 108a b c)d - 2b c - 18a b c +--R (4) --------------------------------------------------------------- +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=1/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*d/((b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*_ + (c+d*x)^(3/2))+32/3*b*d^2*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 32b d x + (48a b d + 48b c d )x + (12a b d + 72a b c d + 12b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a d + 18a b c d + 18a b c d - 2b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 3 3 3 2 2 3 2 3 3 2 2 +--R 160a b c d x + (240a b c d + 240a b c d )x +--R + +--R 4 2 3 3 2 3 2 2 3 4 5 2 3 4 3 2 +--R (60a b c d + 360a b c d + 60a b c d)x - 10a c d + 90a b c d +--R + +--R 3 2 4 2 3 5 +--R 90a b c d - 10a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 2 4 2 5 2 3 2 3 3 4 +--R (- a b c - 25a b )d + (9a b c + 225a b c)d +--R + +--R 4 3 2 4 2 3 5 4 5 3 2 +--R (9a b c + 225a b c )d + (- b c - 25a b c )d +--R * +--R 4 +--R x +--R + +--R 4 5 5 3 2 2 4 2 4 +--R (- 2a b c - 50a b)d + (16a b c + 400a b c)d +--R + +--R 2 3 3 3 3 2 3 4 4 2 4 3 2 +--R (36a b c + 900a b c )d + (16a b c + 400a b c )d +--R + +--R 5 5 5 4 +--R (- 2b c - 50a b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 5 4 2 5 4 3 2 3 4 2 2 3 +--R (- a c - 25a )d + (5a b c + 125a b c)d + (44a b c + 1100a b c )d +--R + +--R 2 3 4 3 3 3 2 4 5 2 4 4 5 6 5 5 +--R (44a b c + 1100a b c )d + (5a b c + 125a b c )d - b c - 25a b c +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 2a c - 50a c)d + (16a b c + 400a b c )d +--R + +--R 3 2 4 4 2 3 2 2 3 5 3 3 4 4 6 2 4 5 +--R (36a b c + 900a b c )d + (16a b c + 400a b c )d - 2a b c - 50a b c +--R * +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 3 2 5 4 2 4 +--R (- a c - 25a c )d + (9a b c + 225a b c )d + (9a b c + 225a b c )d +--R + +--R 2 3 6 3 3 5 +--R - a b c - 25a b c +--R / +--R 6 2 2 6 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2 4 +--R (15a b c d - 60a b c d + 90a b c d - 60a b c d + 15a b c d )x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 +--R 30a b c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d +--R + +--R 2 6 7 +--R 30a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 6 6 2 4 4 5 3 5 3 4 4 6 2 2 6 8 2 +--R (15a c d - 135a b c d + 240a b c d - 135a b c d + 15a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R (30a c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d + 30a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 2 3 2 2 2 3 4 +--R (- a c - 25a )d + (9a b c + 225a b c)d + (9a b c + 225a b c )d - b c +--R + +--R 3 3 +--R - 25a b c +--R / +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=1/(x*(a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=2/3*b/(a*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-2*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+_ + 2*b*(b*c-3*a*d)/(a^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 2/3*d*(3*b^2*c^2-10*a*b*c*d-a^2*d^2)*sqrt(a+b*x)/(a^2*c*(b*c-a*d)^3*_ + (c+d*x)^(3/2))+2/3*d*(b*c+a*d)*(3*b^2*c^2-14*a*b*c*d+3*a^2*d^2)*_ + sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (- 6a b d + 24a b c d - 36a b c d + 24a b c d - 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 6a d + 18a b c d - 12a b c d - 12a b c d + 18a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (6a b d - 22a b c d - 22a b c d + 6b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b d - 36a b c d - 48a b c d - 36a b c d + 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 6a b c d - 48a b c d - 48a b c d - 6a b c d + 6b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R 8a c d - 24a b c d - 24a b c d + 8a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 2 5 6 2 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=1/(x^2*(a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-1/3*b*(5*b*c-3*a*d)/(a^2*c*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1)/_ + (a*c*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5*(b*c+a*d)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_ + b*(5*b^2*c^2-10*a*b*c*d+a^2*d^2)/(a^3*c*(b*c-a*d)^2*(c+d*x)^(3/2)*_ + sqrt(a+b*x))-1/3*d*(15*b^3*c^3-35*a*b^2*c^2*d+9*a^2*b*c*d^2-_ + 5*a^3*d^3)*sqrt(a+b*x)/(a^3*c^2*(b*c-a*d)^3*(c+d*x)^(3/2))-_ + 1/3*d*(15*b^4*c^4-40*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+_ + 15*a^4*d^4)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 6 5 +--R 15b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 15a d - 30a b c d - 15a b c d + 60a b c d - 15a b c d +--R + +--R 5 5 6 6 +--R - 30a b c d + 15b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 15a c d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 5 6 +--R 15a b c +--R * +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (- 15a b d + 40a b c d - 18a b c d + 40a b c d - 15b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 30a b d + 60a b c d + 18a b c d + 18a b c d + 60a b c d +--R + +--R 6 5 +--R - 30b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (- 15a d + 87a b c d - 48a b c d + 87a b c d - 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 20a c d + 48a b c d - 12a b c d - 12a b c d + 48a b c d +--R + +--R 5 6 +--R - 20a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R - 3a c d + 12a b c d - 18a b c d + 12a b c d - 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 3 5 7 3 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 2 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R (3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=1/(x^3*(a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 7 2 2 6 2 2 2 2 5 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 4 2 2 3 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=1/12*b*(35*b^2*c^2-6*a*b*c*d-21*a^2*d^2)/(a^3*c^2*(b*c-a*d)*_ + (a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1/2)/(a*c*x^2*(a+b*x)^(3/2)*_ + (c+d*x)^(3/2))+7/4*(b*c+a*d)/(a^2*c^2*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))-_ + 5/4*(7*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_ + (sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))+1/4*b*(35*b^3*c^3-_ + 55*a*b^2*c^2*d-3*a^2*b*c*d^2+7*a^3*d^3)/(a^4*c^2*(b*c-a*d)^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(105*b^4*c^4-200*a*b^3*c^3*d+_ + 18*a^2*b^2*c^2*d^2+48*a^3*b*c*d^3-35*a^4*d^4)*sqrt(a+b*x)/_ + (a^4*c^3*(b*c-a*d)^3*(c+d*x)^(3/2))+1/12*d*(b*c+a*d)*(105*b^4*c^4-_ + 340*a*b^3*c^3*d+406*a^2*b^2*c^2*d^2-340*a^3*b*c*d^3+105*a^4*d^4)*_ + sqrt(a+b*x)/(a^4*c^4*(b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 105a b d + 270a b c d - 135a b c d - 60a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 135a b c d + 270a b c d - 105b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 105a d + 165a b c d + 135a b c d - 195a b c d - 195a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 135a b c d + 165a b c d - 105b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R - 105a c d + 270a b c d - 135a b c d - 60a b c d +--R + +--R 3 4 5 2 2 5 6 6 7 +--R - 135a b c d + 270a b c d - 105a b c +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 105a b d - 235a b c d + 66a b c d + 66a b c d - 235a b c d +--R + +--R 7 5 2 +--R 105b c d +--R * +--R 5 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 210a b d - 330a b c d - 186a b c d + 228a b c d - 186a b c d +--R + +--R 6 5 2 7 6 +--R - 330a b c d + 210b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 105a d + 45a b c d - 549a b c d + 207a b c d + 207a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 549a b c d + 45a b c d + 105b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R 140a c d - 276a b c d - 12a b c d + 168a b c d - 12a b c d +--R + +--R 2 5 6 6 7 +--R - 276a b c d + 140a b c +--R * +--R 2 +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 21a c d - 63a b c d + 42a b c d + 42a b c d - 63a b c d +--R + +--R 2 5 7 +--R 21a b c +--R * +--R x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 8 4 5 7 2 5 4 6 3 6 3 5 4 7 2 4 5 8 4 +--R (12a b c d - 48a b c d + 72a b c d - 48a b c d + 12a b c d)x +--R + +--R 9 4 5 8 5 4 7 2 6 3 6 3 7 2 5 4 8 +--R 12a c d - 36a b c d + 24a b c d + 24a b c d - 36a b c d +--R + +--R 4 5 9 +--R 12a b c +--R * +--R 3 +--R x +--R + +--R 9 5 4 8 6 3 7 2 7 2 6 3 8 5 4 9 2 +--R (12a c d - 48a b c d + 72a b c d - 48a b c d + 12a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=x^2*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (1) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=1/3*x^3*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R 3 +-------+ +--R x \|b x + a +--R (2) ------------- +--R +---------+ +--R 3\|- b x - a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 +---------+ +-------+ +--R x \|- b x - a \|b x + a +--R (3) - ------------------------ +--R 3b x + 3a +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=x*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R x\|b x + a +--R (1) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=1/2*x^2*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (2) ------------- +--R +---------+ +--R 2\|- b x - a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +---------+ +-------+ +--R x \|- b x - a \|b x + a +--R (3) - ------------------------ +--R 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=x*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R x\|b x + a +--R (2) ------------ +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +-------+ +--R x\|- b x - a \|b x + a +--R (3) - ----------------------- +--R b x + a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=sqrt(a+b*x)/(x*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ------------- +--R +---------+ +--R x\|- b x - a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=log(x)*sqrt(a+b*x)/sqrt(-a-b*x) +--R +--R +--R +-------+ +--R log(x)\|b x + a +--R (2) ---------------- +--R +---------+ +--R \|- b x - a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=sqrt(a+b*x)/(x^2*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------- +--R 2 +---------+ +--R x \|- b x - a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=-sqrt(a+b*x)/(x*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (2) - ------------- +--R +---------+ +--R x\|- b x - a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=sqrt(a+b*x)/(x^3*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------- +--R 3 +---------+ +--R x \|- b x - a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-1/2*sqrt(a+b*x)/(x^2*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (2) - --------------- +--R 2 +---------+ +--R 2x \|- b x - a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 "Error detected within library code: Shouldn't happen" +a0:=integrate(t0,x) +--R +--R +--R 2 +---------+ +-------+ +--R (- x + 1)\|- b x - a \|b x + a +--R (3) -------------------------------- +--R 3 2 +--R 2b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R \|b x + a +--R (4) ------------- +--R +---------+ +--R 2\|- b x - a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=sqrt(a+b*x)/(x^m*sqrt(-a-b*x)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------- +--R m +---------+ +--R x \|- b x - a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=x^(1-m)*sqrt(a+b*x)/((1-m)*sqrt(-a-b*x)) +--R +--R +--R - m + 1 +-------+ +--R x \|b x + a +--R (2) - ------------------- +--R +---------+ +--R (m - 1)\|- b x - a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=x^2*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R 2 n +--R x (b x + a) +--R (1) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=1/3*x^3*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R 3 n +--R x (b x + a) +--R (2) ------------- +--R n +--R 3(- b x - a) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R x cos(n %pi) +--R (3) --------------------------- +--R 2 2 +--R 3sin(n %pi) + 3cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R 3 2 3 2 n 3 n +--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a) +--R (4) ---------------------------------------------------------------------- +--R 2 2 n +--R (3sin(n %pi) + 3cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 2 2 n +--R (- 3x sin(n %pi) - 3x cos(n %pi) )(- b x - a) +--R + +--R 3 2 3 2 n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 3 2 3 2 n n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R 2 n 2 +--R 3x cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (3sin(n %pi) + 3cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=x*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R n +--R x (b x + a) +--R (1) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=1/2*x^2*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R 2 n +--R x (b x + a) +--R (2) ------------- +--R n +--R 2(- b x - a) +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R x cos(n %pi) +--R (3) --------------------------- +--R 2 2 +--R 2sin(n %pi) + 2cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 2 2 n 2 n +--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a) +--R (4) ---------------------------------------------------------------------- +--R 2 2 n +--R (2sin(n %pi) + 2cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- 2x sin(n %pi) - 2x cos(n %pi) )(- b x - a) +--R + +--R 2 2 2 2 n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 2 2 n n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R 2x cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (2sin(n %pi) + 2cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(a+b*x)^n/(-a-b*x)^n +--R +--R +--R n +--R (b x + a) +--R (1) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=x*(a+b*x)^n/(-a-b*x)^n +--R +--R +--R n +--R x (b x + a) +--R (2) ------------ +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R x cos(n %pi) +--R (3) ------------------------- +--R 2 2 +--R sin(n %pi) + cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 n n +--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a) +--R (4) ---------------------------------------------------------------------- +--R 2 2 n +--R (sin(n %pi) + cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- sin(n %pi) - cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n n - 1 +--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (sin(n %pi) + cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(a+b*x)^n/(x*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=(a+b*x)^n*log(x)/(-a-b*x)^n +--R +--R +--R n +--R log(x)(b x + a) +--R (2) ---------------- +--R n +--R (- b x - a) +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R cos(n %pi)log(x) +--R (3) ------------------------- +--R 2 2 +--R sin(n %pi) + cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n +--R (- log(x)sin(n %pi) - cos(n %pi) log(x))(b x + a) +--R + +--R n +--R cos(n %pi)log(x)(- b x - a) +--R / +--R 2 2 n +--R (sin(n %pi) + cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- sin(n %pi) - cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (- b n x log(x)sin(n %pi) - b n x cos(n %pi) log(x))(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n +--R (- b n x log(x)sin(n %pi) - b n x cos(n %pi) log(x))(- b x - a) +--R * +--R n - 1 +--R (b x + a) +--R + +--R n 2 +--R cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 +--R (x sin(n %pi) + x cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(a+b*x)^n/(x^2*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R 2 n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-(a+b*x)^n/(x*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (2) - -------------- +--R n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R cos(n %pi) +--R (3) - ----------------------------- +--R 2 2 +--R x sin(n %pi) + x cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 n n +--R (sin(n %pi) + cos(n %pi) )(b x + a) - cos(n %pi)(- b x - a) +--R (4) -------------------------------------------------------------- +--R 2 2 n +--R (x sin(n %pi) + x cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- sin(n %pi) - cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R cos(n %pi)((- b x - a) ) +--R / +--R 2 2 2 2 n 2 +--R (x sin(n %pi) + x cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(a+b*x)^n/(x^3*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R 3 n +--R x (- b x - a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1/2*(a+b*x)^n/(x^2*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (2) - --------------- +--R 2 n +--R 2x (- b x - a) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R cos(n %pi) +--R (3) - ------------------------------- +--R 2 2 2 2 +--R 2x sin(n %pi) + 2x cos(n %pi) +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R 2 2 n n +--R (sin(n %pi) + cos(n %pi) )(b x + a) - cos(n %pi)(- b x - a) +--R (4) -------------------------------------------------------------- +--R 2 2 2 2 n +--R (2x sin(n %pi) + 2x cos(n %pi) )(- b x - a) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n +--R (- 2sin(n %pi) - 2cos(n %pi) )(- b x - a) +--R + +--R 2 2 n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n n - 1 +--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) (b x + a) +--R + +--R n 2 +--R 2cos(n %pi)((- b x - a) ) +--R / +--R 3 2 3 2 n 2 +--R (2x sin(n %pi) + 2x cos(n %pi) )((- b x - a) ) +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(a+b*x)^n/(x^m*(-a-b*x)^n) +--R +--R +--R n +--R (b x + a) +--R (1) -------------- +--R n m +--R (- b x - a) x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=x^(1-m)*(a+b*x)^n/((1-m)*(-a-b*x)^n) +--R +--R +--R - m + 1 n +--R x (b x + a) +--R (2) - ------------------- +--R n +--R (m - 1)(- b x - a) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R x cos(n %pi) +--R (3) - --------------------------------------------------- +--R 2 2 m log(x) +--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )%e +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 - m + 1 n m log(x) +--R (sin(n %pi) + cos(n %pi) )x (b x + a) %e +--R + +--R n +--R - x cos(n %pi)(- b x - a) +--R / +--R 2 2 n m log(x) +--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )(- b x - a) %e +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 n - 1 - m + 1 +--R (b n sin(n %pi) + b n cos(n %pi) )(- b x - a) x +--R + +--R 2 2 n - m +--R ((- m + 1)sin(n %pi) + (- m + 1)cos(n %pi) )(- b x - a) x +--R * +--R n +--R (b x + a) +--R + +--R 2 2 n - m + 1 n - 1 +--R (b n sin(n %pi) + b n cos(n %pi) )(- b x - a) x (b x + a) +--R * +--R m log(x) +--R %e +--R + +--R n 2 +--R (m - 1)cos(n %pi)((- b x - a) ) +--R / +--R 2 2 n 2 m log(x) +--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )((- b x - a) ) %e +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=x^3*sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R 3 +-----+ +--R x \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+11/2*asin(x)-6*sqrt(1+x)/sqrt(1-x)-_ + 3*sqrt(1-x)*sqrt(1+x)-1/2*x*sqrt(1-x^2),11/2*asin(x)+2/3*x^3*_ + sqrt(1+x)/(1-x)^(3/2)-13/3*x^2*sqrt(1+x)/sqrt(1-x)-13/3*sqrt(1-x)*_ + sqrt(1+x)-1/6*(26+33*x)*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R [ +--R 2 +-----+ +--R (18x - 74x + 52)\|x + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R ((- 3x + 3x)\|- x + 1 + (33x - 33)asin(x))\|- x + 1 +--R / +--R +-------+ +--R (6x - 6)\|- x + 1 +--R , +--R 3 2 +-----+ +-------+ +--R (3x + 12x - 71x + 52)\|x + 1 + (33x - 33)asin(x)\|- x + 1 +--R -------------------------------------------------------------] +--R +-------+ +--R (6x - 6)\|- x + 1 +--R Type: Tuple(Expression(Integer)) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=x^2*sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R x \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x)-4*sqrt(1+x)/sqrt(1-x)-_ + sqrt(1-x)*sqrt(1+x),1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x)-_ + 2*(1+x)^(3/2)/sqrt(1-x)-3*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R [----------------------------------------------------, +--R +-------+ +--R (3x - 3)\|- x + 1 +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R ----------------------------------------------------] +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Tuple(Expression(Integer)) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=x*sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x)-2*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-----+ +-------+ +--R (- 7x + 5)\|x + 1 + (3x - 3)asin(x)\|- x + 1 +--R (2) ---------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 500 +--m0:=a0-r0 +--E 234 + +--S 235 of 500 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 500 +t0:=sqrt(1+x)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (2) ------------------ +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-----+ 2 +--R (8x + 8)\|- x + 1 \|x + 1 - 17x + 34x - 17 +--R (3) -------------------------------------------- +--R 2 +--R 24x - 48x + 24 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 17 +--R (4) - -- +--R 24 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=sqrt(1+x)/(-1+x)^(5/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) --------------------- +--R 2 +-----+ +--R (x - 2x + 1)\|x - 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-1/3*(1+x)^(3/2)/(-1+x)^(3/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (2) ----------------- +--R +-----+ +--R (3x - 3)\|x - 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ 2 +--R (- 3x - 3)\|x - 1 \|x + 1 + 4x - 8x + 4 +--R (3) ----------------------------------------- +--R 2 +--R 9x - 18x + 9 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - +--R 9 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=sqrt(1+x)/((1-x)^(5/2)*x) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ------------------------ +--R 3 2 +-------+ +--R (x - 2x + x)\|- x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=-2*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/(1-x)^(3/2)+_ + 5/3*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-------+ +--R +-------+ \|- x + 1 +-----+ +--R (- 6x + 6)\|- x + 1 atanh(----------) + (5x - 7)\|x + 1 +--R +-----+ +--R \|x + 1 +--R (2) -------------------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-----+ +--R 2 - \|- x + 1 \|x + 1 - 1 +--R (- 3x + 6x - 3)log(------------------------) +--R x +--R + +--R +-------+ +-----+ 2 +--R (- 5x + 7)\|- x + 1 \|x + 1 - 3x + 6x - 3 +--R / +--R 2 +--R 3x - 6x + 3 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-------+ +-----+ +-------+ +--R - \|- x + 1 \|x + 1 - 1 \|- x + 1 +--R (4) - log(------------------------) + 2atanh(----------) - 1 +--R x +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=sqrt(1+x)/((1-x)^(5/2)*x^2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ------------------------- +--R 4 3 2 +-------+ +--R (x - 2x + x )\|- x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=-6*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x)+_ + 3*sqrt(1+x)/(x*sqrt(1-x))-14/3*sqrt(1-x)*sqrt(1+x)/x +--R +--R +--R +-------+ +--R 2 +-------+ \|- x + 1 2 +-----+ +--R (- 18x + 18x)\|- x + 1 atanh(----------) + (14x - 19x + 3)\|x + 1 +--R +-----+ +--R \|x + 1 +--R (2) -------------------------------------------------------------------- +--R 2 +-------+ +--R (3x - 3x)\|- x + 1 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-----+ +--R 3 2 \|- x + 1 \|x + 1 + 1 +--R (- 144x + 288x - 144x)log(----------------------) +--R x +--R + +--R 2 +-------+ +-----+ 3 2 +--R (- 224x + 304x - 48)\|- x + 1 \|x + 1 + 273x - 546x + 273x +--R / +--R 3 2 +--R 48x - 96x + 48x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-------+ +-----+ +-------+ +--R \|- x + 1 \|x + 1 + 1 \|- x + 1 +--R - 48log(----------------------) + 96atanh(----------) + 91 +--R x +-----+ +--R \|x + 1 +--R (4) ---------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=sqrt(1+x)/((1-x)^(5/2)*x^3) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ------------------------- +--R 5 4 3 +-------+ +--R (x - 2x + x )\|- x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-11*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x^2)+_ + 13/3*sqrt(1+x)/(x^2*sqrt(1-x))-11/2*sqrt(1-x)*sqrt(1+x)/x^2-_ + 26/3*sqrt(1-x)*sqrt(1+x)/x +--R +--R +--R (2) +--R +-------+ +--R 3 2 +-------+ \|- x + 1 3 2 +-----+ +--R (- 66x + 66x )\|- x + 1 atanh(----------) + (52x - 71x + 12x + 3)\|x + 1 +--R +-----+ +--R \|x + 1 +--R ---------------------------------------------------------------------------- +--R 3 2 +-------+ +--R (6x - 6x )\|- x + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-----+ +--R 4 3 2 - \|- x + 1 \|x + 1 - 1 +--R (- 528x + 1056x - 528x )log(------------------------) +--R x +--R + +--R 3 2 +-------+ +-----+ 4 3 2 +--R (- 832x + 1136x - 192x - 48)\|- x + 1 \|x + 1 - 159x + 318x - 159x +--R / +--R 4 3 2 +--R 96x - 192x + 96x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-------+ +-----+ +-------+ +--R - \|- x + 1 \|x + 1 - 1 \|- x + 1 +--R - 176log(------------------------) + 352atanh(----------) - 53 +--R x +-----+ +--R \|x + 1 +--R (4) -------------------------------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=x^2/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 2 +--R x +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=1/2*acosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 + acosh(x) +--R (2) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) + x\|x - 1 \|x + 1 +--R (3) ----------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) - acosh(x) +--R (4) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (5) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=x/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R x +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (2) \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R (3) \|x - 1 \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=1/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=acosh(x) +--R +--R +--R (2) acosh(x) +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R (3) - log(- \|x - 1 \|x + 1 + x) +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R (4) - log(- \|x - 1 \|x + 1 + x) - acosh(x) +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (5) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=1/(x*sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=2*atan(sqrt(-1+x)/sqrt(1+x)) +--R +--R +--R +-----+ +--R \|x - 1 +--R (2) 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 +--R (3) atan(-----------------------) +--R +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 \|x - 1 +--R (4) atan(-----------------------) - 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 \|x + 1 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=1/(x^2*sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 1 +--R (1) ------------------ +--R 2 +-----+ +-----+ +--R x \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=sqrt(-1+x)*sqrt(1+x)/x +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (2) ---------------- +--R x +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 + x +--R (3) -------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) 1 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=x^2*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R 2 +-----+ +-----+ +--R (1) x \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-1/8*acosh(x)-1/8*x*sqrt(-1+x)*sqrt(1+x)+1/4*x^3*sqrt(-1+x)*_ + sqrt(1+x),1/4*(-1+x)^(3/2)*x*(1+x)^(3/2)-1/8*acosh(x)+_ + 1/8*(-1+x)^(3/2)*sqrt(1+x)+1/8*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R (2) +--R 3 +-----+ +-----+ 3 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) (2x - x)\|x - 1 \|x + 1 - acosh(x) +--R [------------------------------------,------------------------------------] +--R 8 8 +--R Type: Tuple(Expression(Integer)) +--E 287 + +--S 288 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ 3 +-----+ +-----+ +--R - log(- \|x - 1 \|x + 1 - x) + (2x - x)\|x - 1 \|x + 1 +--R (3) --------------------------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R - log(- \|x - 1 \|x + 1 - x) + acosh(x) +--R (4) ---------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (5) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 8\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (1) x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=1/3*(-1+x)^(3/2)*(1+x)^(3/2) +--R +--R +--R 2 +-----+ +-----+ +--R (x - 1)\|x - 1 \|x + 1 +--R (2) ------------------------ +--R 3 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R 2 +-----+ +-----+ +--R (x - 1)\|x - 1 \|x + 1 +--R (3) ------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (1) \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=-1/2*acosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x),_ + -1/2*acosh(x)+1/2*(-1+x)^(3/2)*sqrt(1+x)+1/2*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R x\|x - 1 \|x + 1 - acosh(x) x\|x - 1 \|x + 1 - acosh(x) +--R (2) [----------------------------,----------------------------] +--R 2 2 +--R Type: Tuple(Expression(Integer)) +--E 297 + +--S 298 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (- 4x\|x - 1 \|x + 1 - 4x + 2)log(\|x + 1 + \|x - 1 ) +--R + +--R 3 +-----+ +-----+ 4 2 +--R (2x - x)\|x - 1 \|x + 1 + 2x - 2x +--R / +--R +-----+ +-----+ 2 +--R 4x\|x - 1 \|x + 1 + 4x - 2 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R - 2log(\|x + 1 + \|x - 1 ) + acosh(x) +--R (4) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (5) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=sqrt(-1+x)*sqrt(1+x)/x +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) ---------------- +--R x +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=-2*atan(sqrt(-1+x)/sqrt(1+x))+sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +--R \|x - 1 +-----+ +-----+ +--R (2) - 2atan(--------) + \|x - 1 \|x + 1 +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 +-----+ +-----+ +--R (3) - atan(-----------------------) + \|x - 1 \|x + 1 +--R +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 \|x - 1 +--R (4) - atan(-----------------------) + 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 \|x + 1 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=sqrt(-1+x)*sqrt(1+x)/x^2 +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) ---------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=acosh(x)-sqrt(-1+x)*sqrt(1+x)/x +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x acosh(x) +--R (2) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - x log(\|x - 1 \|x + 1 - x) - \|x - 1 \|x + 1 + x +--R (3) ---------------------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +--R (4) - log(\|x - 1 \|x + 1 - x) - acosh(x) + 1 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (5) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/(sqrt(1+2*x)*sqrt(3+2*x)) +--R +--R +--R 1 +--R (1) ------------------ +--R +------+ +------+ +--R \|2x + 1 \|2x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=asinh(sqrt(1+2*x)/sqrt(2)) +--R +--R +--R +------+ +--R \|2x + 1 +--R (2) asinh(---------) +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R log(- \|2x + 1 \|2x + 3 + 2x + 2) +--R (3) - ---------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +------+ +--R +------+ +------+ \|2x + 1 +--R - log(- \|2x + 1 \|2x + 3 + 2x + 2) - 2asinh(---------) +--R +-+ +--R \|2 +--R (4) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/(x*sqrt(-2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +------+ +------+ +--R x\|3x - 2 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=atan(sqrt(3/2)*sqrt(-2+3*x)/sqrt(3+5*x))*sqrt(2/3) +--R +--R +--R +-+ +------+ +--R +-+ \|3 \|3x - 2 +--R \|2 atan(-------------) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (2) ----------------------- +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (- 337x - 4044)\|2 \|3 +--R \|2 \|3 atan(-------------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 + 456x + 5472 +--R (3) --------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (- 337x - 4044)\|2 \|3 +--R \|2 atan(-------------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 + 456x + 5472 +--R + +--R +-+ +------+ +--R +-+ \|3 \|3x - 2 +--R - 2\|2 atan(-------------) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R / +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((-1+x)^(3/2)*x*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 3 +-----+ +-----+ +--R (x - x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=-2*atan(sqrt(-1+x)/sqrt(1+x))+(-1)/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R - 2\|x - 1 \|x + 1 atan(--------) - 1 +--R +-----+ +--R \|x + 1 +--R (2) ------------------------------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 ok to fail. differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+ +-----+ +--R 2 16\|x - 1 \|x + 1 - 63 +-----+ +-----+ 2 +--R (- 12x + 12)atan(-----------------------) - 12\|x - 1 \|x + 1 - 7x + 7 +--R +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 +--R ------------------------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 ok to fail. differs by a constant +m0:=a0-r0 +--R +--R +--R +-----+ +-----+ +-----+ +--R 16\|x - 1 \|x + 1 - 63 \|x - 1 +--R - 12atan(-----------------------) + 24atan(--------) - 7 +--R +-----+ +-----+ +-----+ +--R 63\|x - 1 \|x + 1 + 16 \|x + 1 +--R (4) -------------------------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=x*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-------+ +-----+ +--R (1) x\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1/3*(1-x)^(3/2)*(1+x)^(3/2) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (2) -------------------------- +--R 3 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (3) -------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=x^3*(2+3*x)^(3/2)*(1+4*x)^(1/2) +--R +--R +--R 4 3 +------+ +------+ +--R (1) (3x + 2x )\|3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=22357/6635520*(2+3*x)^(3/2)*(1+4*x)^(3/2)+1/92160*(8-403*x)*_ + (2+3*x)^(3/2)*(1+4*x)^(3/2)-1/960*x^2*(2+3*x)^(3/2)*(1+4*x)^(3/2)+_ + 1/24*x^3*(2+3*x)^(3/2)*(1+4*x)^(3/2)+1067875/84934656*_ + asinh(sqrt(3/5)*sqrt(1+4*x))/sqrt(3)-42715/5308416*(2+3*x)^(3/2)*_ + sqrt(1+4*x)+213575/42467328*sqrt(2+3*x)*sqrt(1+4*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|3 \|4x + 1 +--R 5339375asinh(-------------) +--R +-+ +--R \|5 +--R + +--R 5 4 3 2 +--R 212336640x + 189333504x + 8239104x - 3699456x + 2179184x +--R + +--R - 1763226 +--R * +--R +-+ +------+ +------+ +--R \|3 \|3x + 2 \|4x + 1 +--R / +--R +-+ +--R 424673280\|3 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/(sqrt(-1+a+b*x)*sqrt(1+a+b*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=2*asinh(sqrt(-1+a+b*x)/sqrt(2))/b +--R +--R +--R +-----------+ +--R \|b x + a - 1 +--R 2asinh(--------------) +--R +-+ +--R \|2 +--R (2) ---------------------- +--R b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=x^2*(1+x)^(1/4)/(1-x)^(1/4) +--R +--R +--R 2 4+-----+ +--R x \|x + 1 +--R (1) ---------- +--R 4+-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-3/8*(1-x)^(3/4)*(1+x)^(1/4)-1/12*(1-x)^(3/4)*(1+x)^(5/4)-_ + 1/3*(1-x)^(3/4)*x*(1+x)^(5/4)+3/8*atan(1-(1-x)^(1/4)*sqrt(2)/_ + (1+x)^(1/4))/sqrt(2)-3/8*atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/_ + sqrt(2)-3/16*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/_ + sqrt(1+x))/sqrt(2)+3/16*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+_ + sqrt(1-x)/sqrt(1+x))/sqrt(2) +--R +--R +--R (2) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R 9log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - 9log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+ +--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1 +--R - 18atan(-------------------------) + 18atan(-------------------------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 2 +-+4+-------+3 4+-----+ +--R (- 16x - 20x - 22)\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 48\|2 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=x*(1+x)^(1/4)/(1-x)^(1/4) +--R +--R +--R 4+-----+ +--R x\|x + 1 +--R (1) ---------- +--R 4+-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-1/4*(1-x)^(3/4)*(1+x)^(1/4)-1/2*(1-x)^(3/4)*(1+x)^(5/4)+_ + 1/4*atan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_ + 1/4*atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_ + 1/8*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/_ + sqrt(2)+1/8*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+_ + sqrt(1-x)/sqrt(1+x))/sqrt(2) +--R +--R +--R (2) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+ +--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1 +--R - 2atan(-------------------------) + 2atan(-------------------------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+4+-------+3 4+-----+ +--R (- 4x - 6)\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1+x)^(1/4)/(1-x)^(1/4) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ---------- +--R 4+-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-(1-x)^(3/4)*(1+x)^(1/4)+atan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/_ + sqrt(2)-atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_ + 1/2*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/_ + sqrt(2)+1/2*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/_ + sqrt(1+x))/sqrt(2) +--R +--R +--R (2) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+ +--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1 +--R - 2atan(-------------------------) + 2atan(-------------------------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+4+-------+3 4+-----+ +--R - 2\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ----------- +--R 4+-------+ +--R x\|- x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-2*atan((1+x)^(1/4)/(1-x)^(1/4))-2*atanh((1+x)^(1/4)/(1-x)^(1/4))-_ + log(1-(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4)+sqrt(1+x)/sqrt(1-x))/_ + sqrt(2)+log(1+(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4)+sqrt(1+x)/_ + sqrt(1-x))/sqrt(2)-atan(1-(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4))*_ + sqrt(2)+atan(1+(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4))*sqrt(2) +--R +--R +--R (2) +--R +-+ +-------+4+-----+ 4+-------+ +-----+ +-------+4+-------+ +--R \|2 \|- x + 1 \|x + 1 + \|- x + 1 \|x + 1 + \|- x + 1 \|- x + 1 +--R log(------------------------------------------------------------------) +--R +-------+4+-------+ +--R \|- x + 1 \|- x + 1 +--R + +--R - +--R log +--R +-+ +-------+4+-----+ 4+-------+ +-----+ +--R - \|2 \|- x + 1 \|x + 1 + \|- x + 1 \|x + 1 +--R + +--R +-------+4+-------+ +--R \|- x + 1 \|- x + 1 +--R / +--R +-------+4+-------+ +--R \|- x + 1 \|- x + 1 +--R + +--R 4+-----+ +-+4+-----+ 4+-------+ +--R +-+ \|x + 1 \|2 \|x + 1 + \|- x + 1 +--R - 2\|2 atanh(----------) + 2atan(-------------------------) +--R 4+-------+ 4+-------+ +--R \|- x + 1 \|- x + 1 +--R + +--R +-+4+-----+ 4+-------+ 4+-----+ +--R \|2 \|x + 1 - \|- x + 1 +-+ \|x + 1 +--R 2atan(-------------------------) - 2\|2 atan(----------) +--R 4+-------+ 4+-------+ +--R \|- x + 1 \|- x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^2) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ------------ +--R 2 4+-------+ +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-(1-x)^(3/4)*(1+x)^(1/4)/x+atan((1-x)^(1/4)/(1+x)^(1/4))-_ + atanh((1-x)^(1/4)/(1+x)^(1/4)) +--R +--R +--R 4+-------+ 4+-------+ +--R \|- x + 1 \|- x + 1 4+-------+3 4+-----+ +--R - x atanh(----------) + x atan(----------) - \|- x + 1 \|x + 1 +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R (2) ---------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^3) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ------------ +--R 3 4+-------+ +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-1/2*(1-x)^(3/4)*(1+x)^(1/4)/x^2-3/4*(1-x)^(3/4)*(1+x)^(1/4)/x+_ + 1/4*atan((1-x)^(1/4)/(1+x)^(1/4))-1/4*atanh((1-x)^(1/4)/(1+x)^(1/4)) +--R +--R +--R (2) +--R 4+-------+ 4+-------+ +--R 2 \|- x + 1 2 \|- x + 1 4+-------+3 4+-----+ +--R - x atanh(----------) + x atan(----------) + (- 3x - 2)\|- x + 1 \|x + 1 +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R -------------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^4) +--R +--R +--R 4+-----+ +--R \|x + 1 +--R (1) ------------ +--R 4 4+-------+ +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-1/3*(1-x)^(3/4)*(1+x)^(1/4)/x^3-5/12*(1-x)^(3/4)*(1+x)^(1/4)/x^2-_ + 11/24*(1-x)^(3/4)*(1+x)^(1/4)/x+3/8*atan((1-x)^(1/4)/(1+x)^(1/4))-_ + 3/8*atanh((1-x)^(1/4)/(1+x)^(1/4)) +--R +--R +--R (2) +--R 4+-------+ 4+-------+ +--R 3 \|- x + 1 3 \|- x + 1 +--R - 9x atanh(----------) + 9x atan(----------) +--R 4+-----+ 4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 2 4+-------+3 4+-----+ +--R (- 11x - 10x - 8)\|- x + 1 \|x + 1 +--R / +--R 3 +--R 24x +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=x^3*(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 3 4+-------+ +--R x \|b x + a +--R (1) ------------ +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-1/1536*(585*b^3*c^3-63*a*b^2*c^2*d-61*a^2*b*c*d^2-77*a^3*d^3)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^4)-1/384*(10*a*c-_ + 117*b*c^2/d+11*a^2*d/b)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)-_ + 1/48*(13*b*c-a*d)*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+_ + 1/4*x^3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/d+1/1024*(b*c-a*d)*_ + (195*b^3*c^3+135*a*b^2*c^2*d+105*a^2*b*c*d^2+77*a^3*d^3)*_ + atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*_ + d^(17/4))+1/1024*(b*c-a*d)*(195*b^3*c^3+135*a*b^2*c^2*d+_ + 105*a^2*b*c*d^2+77*a^3*d^3)*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(17/4)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 231a d - 84a b c d - 90a b c d - 180a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 231a d - 84a b c d - 90a b c d - 180a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 768b d x + (64a b d - 832b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 88a b d - 80a b c d + 936b c d)x + 154a d + 122a b c d +--R + +--R 2 2 3 3 +--R 126a b c d - 1170b c +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 4 4+-+3 4+-+ +--R 3072b d \|b \|d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=x^2*(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 2 4+-------+ +--R x \|b x + a +--R (1) ------------ +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=1/32*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (b^2*d^3)-1/24*(9*b*c+7*a*d)*(a+b*x)^(5/4)*(c+d*x)^(3/4)/_ + (b^2*d^2)+1/3*x*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)-1/64*_ + (b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*atan(d^(1/4)*_ + (a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4))-_ + 1/64*(b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*_ + atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (21a d + 9a b c d + 15a b c d - 45b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (21a d + 9a b c d + 15a b c d - 45b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 4+-+3 +--R (64b d x + (8a b d - 72b c d)x - 14a d - 12a b c d + 90b c )\|b +--R * +--R 4+-+4+-------+4+-------+3 +--R \|d \|b x + a \|d x + c +--R / +--R 2 3 4+-+3 4+-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=x*(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 4+-------+ +--R x\|b x + a +--R (1) ----------- +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1/8*(5*b*c+3*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+_ + 1/2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)+1/16*(b*c-a*d)*_ + (5*b*c+3*a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(7/4)*d^(9/4))+1/16*(b*c-a*d)*(5*b*c+3*a*d)*_ + atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- 3a d - 2a b c d + 5b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- 3a d - 2a b c d + 5b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R (8b d x + 2a d - 10b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 4+-+3 4+-+ +--R 16b d \|b \|d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(a+b*x)^(1/4)/(c+d*x)^(1/4) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ---------- +--R 4+-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=(a+b*x)^(1/4)*(c+d*x)^(3/4)/d-1/2*(b*c-a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4))-1/2*(b*c-a*d)*_ + atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R (a d - b c)atanh(--------------) + (a d - b c)atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R 2\|b \|d \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2d \|b \|d +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(a+b*x)^(1/4)/(x*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ----------- +--R 4+-------+ +--R x\|d x + c +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-2*a^(1/4)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+_ + 2*b^(1/4)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4)-_ + 2*a^(1/4)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+_ + 2*b^(1/4)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R 4+-+4+-+ \|d \|b x + a 4+-+4+-+ \|c \|b x + a +--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|a \|d x + c +--R + +--R 4+-+4+-------+ 4+-+4+-------+ +--R 4+-+4+-+ \|d \|b x + a 4+-+4+-+ \|c \|b x + a +--R 2\|b \|c atan(--------------) - 2\|a \|d atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|a \|d x + c +--R / +--R 4+-+4+-+ +--R \|c \|d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(a+b*x)^(1/4)/(x^2*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 2 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x)-1/2*(b*c-a*d)*_ + atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(5/4))-_ + 1/2*(b*c-a*d)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(3/4)*c^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|c \|b x + a \|c \|b x + a +--R (a d - b c)x atanh(--------------) + (a d - b c)x atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|a \|d x + c \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R - 2\|a \|c \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2c x \|a \|c +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(a+b*x)^(1/4)/(x^3*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 3 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^2)-1/8*(b*c-5*a*d)*(a+b*x)^(1/4)*_ + (c+d*x)^(3/4)/(a*c^2*x)+1/16*(b*c-a*d)*(3*b*c+5*a*d)*_ + atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(7/4)*c^(9/4))+1/16*(b*c-a*d)*(3*b*c+5*a*d)*atanh(c^(1/4)*_ + (a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d + 2a b c d + 3b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d + 2a b c d + 3b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R ((10a d - 2b c)x - 8a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 4+-+3 4+-+ +--R 16a c x \|a \|c +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(a+b*x)^(1/4)/(x^4*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 4 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^3)-1/24*(b*c-9*a*d)*(a+b*x)^(1/4)*_ + (c+d*x)^(3/4)/(a*c^2*x^2)+1/96*(7*b*c-15*a*d)*(b*c+3*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^3*x)-1/64*(b*c-a*d)*_ + (7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*atan(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4))-1/64*(b*c-a*d)*_ + (7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d - 15a b c d - 9a b c d - 21b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d - 15a b c d - 9a b c d - 21b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 90a d + 12a b c d + 14b c )x + (72a c d - 8a b c )x - 64a c ) +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|a \|c \|b x + a \|d x + c +--R / +--R 2 3 3 4+-+3 4+-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(a+b*x)^(1/4)/(x^5*(c+d*x)^(1/4)) +--R +--R +--R 4+-------+ +--R \|b x + a +--R (1) ------------ +--R 5 4+-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-1/4*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^4)-1/48*(b*c-13*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c^2*x^3)+1/384*(11*b^2*c^2+_ + 10*a*b*c*d-117*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (a^2*c^3*x^2)-1/1536*(77*b^3*c^3+61*a*b^2*c^2*d+63*a^2*b*c*d^2-_ + 585*a^3*d^3)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^3*c^4*x)+_ + 1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+135*a^2*b*c*d^2+_ + 195*a^3*d^3)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(15/4)*c^(17/4))+1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+_ + 135*a^2*b*c*d^2+195*a^3*d^3)*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(17/4)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 585a d + 180a b c d + 90a b c d + 84a b c d + 231b c )x +--R * +--R 4+-+4+-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 585a d + 180a b c d + 90a b c d + 84a b c d + 231b c )x +--R * +--R 4+-+4+-------+ +--R \|c \|b x + a +--R atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (1170a d - 126a b c d - 122a b c d - 154b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 +--R (- 936a c d + 80a b c d + 88a b c )x + (832a c d - 64a b c )x +--R + +--R 3 3 +--R - 768a c +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 4 4 4+-+3 4+-+ +--R 3072a c x \|a \|c +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=x^4/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-1/1536*(585*b^3*c^3+657*a*b^2*c^2*d+803*a^2*b*c*d^2+1155*a^3*d^3)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^4*d^4)+1/384*(117*b^2*c^2+_ + 134*a*b*c*d+165*a^2*d^2)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^3)-_ + 1/48*(13*b*c+15*a*d)*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+_ + 1/4*x^3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/1024*(195*b^4*c^4+_ + 180*a*b^3*c^3*d+210*a^2*b^2*c^2*d^2+308*a^3*b*c*d^3+1155*a^4*d^4)*_ + atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(19/4)*d^(17/4))+_ + 1/1024*(195*b^4*c^4+180*a*b^3*c^3*d+210*a^2*b^2*c^2*d^2+_ + 308*a^3*b*c*d^3+1155*a^4*d^4)*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(19/4)*d^(17/4)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (3465a d + 924a b c d + 630a b c d + 540a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (3465a d + 924a b c d + 630a b c d + 540a b c d + 585b c ) +--R * +--R 4+-+4+-------+ +--R \|d \|b x + a +--R atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 768b d x + (- 960a b d - 832b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (1320a b d + 1072a b c d + 936b c d)x - 2310a d - 1606a b c d +--R + +--R 2 2 3 3 +--R - 1314a b c d - 1170b c +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 4 4+-+3 4+-+ +--R 3072b d \|b \|d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=x^3/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=1/96*(45*b^2*c^2+54*a*b*c*d+77*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (b^3*d^3)-1/24*(9*b*c+11*a*d)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (b^2*d^2)+1/3*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-_ + 1/64*(15*b^3*c^3+15*a*b^2*c^2*d+21*a^2*b*c*d^2+77*a^3*d^3)*_ + atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(15/4)*d^(13/4))-1/64*(15*b^3*c^3+15*a*b^2*c^2*d+_ + 21*a^2*b*c*d^2+77*a^3*d^3)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(15/4)*d^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 231a d - 63a b c d - 45a b c d - 45b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 231a d - 63a b c d - 45a b c d - 45b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (64b d x + (- 88a b d - 72b c d)x + 154a d + 108a b c d + 90b c ) +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 3 4+-+3 4+-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=x^2/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=-1/8*(5*b*c+7*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+_ + 1/2*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/16*(5*b^2*c^2+_ + 6*a*b*c*d+21*a^2*d^2)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(11/4)*d^(9/4))+1/16*(5*b^2*c^2+6*a*b*c*d+_ + 21*a^2*d^2)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(11/4)*d^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (21a d + 6a b c d + 5b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (21a d + 6a b c d + 5b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R (8b d x - 14a d - 10b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 2 4+-+3 4+-+ +--R 16b d \|b \|d +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=x/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R x +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-1/2*(b*c+3*a*d)*atan(d^(1/4)*_ + (a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(5/4))-_ + 1/2*(b*c+3*a*d)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(7/4)*d^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R (- 3a d - b c)atanh(--------------) + (- 3a d - b c)atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R 2\|b \|d \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2b d \|b \|d +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=1/((a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) --------------------- +--R 4+-------+3 4+-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=2*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_ + (b^(3/4)*d^(1/4))+2*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(1/4)) +--R +--R +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R 2atanh(--------------) + 2atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R (2) ---------------------------------------------- +--R 4+-+3 4+-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=1/(x*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-2*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(3/4)*c^(1/4))-2*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(1/4)) +--R +--R +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|c \|b x + a \|c \|b x + a +--R - 2atanh(--------------) - 2atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|a \|d x + c \|a \|d x + c +--R (2) ------------------------------------------------ +--R 4+-+3 4+-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=1/(x^2*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x)+1/2*(3*b*c+a*d)*_ + atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(5/4))+_ + 1/2*(3*b*c+a*d)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(7/4)*c^(5/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|c \|b x + a \|c \|b x + a +--R (a d + 3b c)x atanh(--------------) + (a d + 3b c)x atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|a \|d x + c \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R - 2\|a \|c \|b x + a \|d x + c +--R / +--R 4+-+3 4+-+ +--R 2a c x \|a \|c +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=1/(x^3*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^2)+1/8*(7*b*c+5*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x)-1/16*(21*b^2*c^2+_ + 6*a*b*c*d+5*a^2*d^2)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*_ + (c+d*x)^(1/4)))/(a^(11/4)*c^(9/4))-1/16*(21*b^2*c^2+6*a*b*c*d+_ + 5*a^2*d^2)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(11/4)*c^(9/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d - 6a b c d - 21b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 5a d - 6a b c d - 21b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+3 4+-+4+-------+4+-------+3 +--R ((10a d + 14b c)x - 8a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 2 4+-+3 4+-+ +--R 16a c x \|a \|c +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=1/(x^4*(a+b*x)^(3/4)*(c+d*x)^(1/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 4+-------+3 4+-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^3)+1/24*(11*b*c+9*a*d)*_ + (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x^2)-_ + 1/96*(77*b^2*c^2+54*a*b*c*d+45*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_ + (a^3*c^3*x)+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+15*a^2*b*c*d^2+_ + 15*a^3*d^3)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_ + (a^(15/4)*c^(13/4))+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+_ + 15*a^2*b*c*d^2+15*a^3*d^3)*atanh(c^(1/4)*(a+b*x)^(1/4)/_ + (a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(13/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d + 45a b c d + 63a b c d + 231b c )x atanh(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 4+-+4+-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (45a d + 45a b c d + 63a b c d + 231b c )x atan(--------------) +--R 4+-+4+-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 90a d - 108a b c d - 154b c )x + (72a c d + 88a b c )x - 64a c ) +--R * +--R 4+-+3 4+-+4+-------+4+-------+3 +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 3 3 4+-+3 4+-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=1/((1-a*x)^(1/4)*(1+b*x)^(3/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4+---------+4+-------+3 +--R \|- a x + 1 \|b x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-log(-a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+sqrt(a)+_ + sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + log(a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+_ + sqrt(a)+sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*_ + sqrt(2))+atan(1-b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*_ + (1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4))-atan(1+b^(1/4)*_ + (1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*(1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4)) +--R +--R +--R (2) +--R log +--R +-+ +-------+ +---------+ +-+ 4+-------+ +--R (\|a \|b x + 1 + \|- a x + 1 \|b )\|b x + 1 +--R + +--R +-+4+---------+4+-+4+-+ +-------+ +--R \|2 \|- a x + 1 \|a \|b \|b x + 1 +--R / +--R +-------+4+-------+ +--R \|b x + 1 \|b x + 1 +--R + +--R - +--R log +--R +-+ +-------+ +---------+ +-+ 4+-------+ +--R (\|a \|b x + 1 + \|- a x + 1 \|b )\|b x + 1 +--R + +--R +-+4+---------+4+-+4+-+ +-------+ +--R - \|2 \|- a x + 1 \|a \|b \|b x + 1 +--R / +--R +-------+4+-------+ +--R \|b x + 1 \|b x + 1 +--R + +--R 4+-+4+-------+ +-+4+---------+4+-+ +--R \|a \|b x + 1 + \|2 \|- a x + 1 \|b +--R - 2atan(-------------------------------------) +--R 4+-+4+-------+ +--R \|a \|b x + 1 +--R + +--R 4+-+4+-------+ +-+4+---------+4+-+ +--R \|a \|b x + 1 - \|2 \|- a x + 1 \|b +--R 2atan(-------------------------------------) +--R 4+-+4+-------+ +--R \|a \|b x + 1 +--R / +--R +-+4+-+4+-+3 +--R \|2 \|a \|b +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=1/((1-a*x)^(1/4)*(1+a*x)^(3/4)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4+---------+4+-------+3 +--R \|- a x + 1 \|a x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-log(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/sqrt(1+a*x))/_ + (a*sqrt(2))+log(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/_ + sqrt(1+a*x))/(a*sqrt(2))+atan(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*_ + sqrt(2)/a-atan(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*sqrt(2)/a +--R +--R +--R (2) +--R +-------+ +---------+ 4+-------+ +-+4+---------+ +-------+ +--R (\|a x + 1 + \|- a x + 1 )\|a x + 1 + \|2 \|- a x + 1 \|a x + 1 +--R log(------------------------------------------------------------------) +--R +-------+4+-------+ +--R \|a x + 1 \|a x + 1 +--R + +--R +-------+ +---------+ 4+-------+ +-+4+---------+ +-------+ +--R (\|a x + 1 + \|- a x + 1 )\|a x + 1 - \|2 \|- a x + 1 \|a x + 1 +--R - log(------------------------------------------------------------------) +--R +-------+4+-------+ +--R \|a x + 1 \|a x + 1 +--R + +--R 4+-------+ +-+4+---------+ +--R \|a x + 1 + \|2 \|- a x + 1 +--R - 2atan(-----------------------------) +--R 4+-------+ +--R \|a x + 1 +--R + +--R 4+-------+ +-+4+---------+ +--R \|a x + 1 - \|2 \|- a x + 1 +--R 2atan(-----------------------------) +--R 4+-------+ +--R \|a x + 1 +--R / +--R +-+ +--R a\|2 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-%i*x)^(1/6*%i)*x^3/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 3 6 +--R x (- %i x + 1) +--R (1) ---------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 476 + +--S 477 of 500 +--r0:=1/4*x^4*AppellF1(4,-1/6*%i,1/6*%i,5,%i*x,-%i*x),(-18/37+3/37*%i)*_ +-- 2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*AppellF1(1+1/6*%i,1/6*%i,_ +-- -3,2+1/6*%i,1/2*(1-%i*x),1-%i*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-%i*x)^(1/6*%i)*x^2/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 2 6 +--R x (- %i x + 1) +--R (1) ---------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 481 + +--S 482 of 500 +--r0:=-1/18*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)+_ +-- 1/3*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)*x+_ +-- (-17/333+34/111*%i)*2^(1/6*%i)*(1+%i*x)^(1-1/6*%i)*_ +-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x)) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-%i*x)^(1/6*%i)*x/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 6 +--R x (- %i x + 1) +--R (1) ---------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 486 + +--S 487 of 500 +--r0:=1/2*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)+_ +-- (-1/37+6/37*%i)*2^(1/6*%i)*(1+%i*x)^(1-1/6*%i)*_ +-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x)) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-%i*x)^(1/6*%i)/(1+%i*x)^(1/6*%i) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 6 +--R (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 491 + +--S 492 of 500 +--r0:=(3/37-18/37*%i)*2^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)*_ +-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x)) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 6 +--R x (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 496 + +--S 497 of 500 +--r0:-(-18/37+3/37*%i)*2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)* +-- AppellF1(1+1/6*%i,1/6*%i,1,2+1/6*%i,1/2*(1-%i*x),1-%i*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} +