diff --git a/changelog b/changelog index bd0d725..2850164 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100604 tpd src/axiom-website/patches.html 20100604.04.tpd.patch +20100604 tpd src/input/Makefile add rule-based algebraic integration +20100604 tpd src/input/richalgebraic000-099.input rule-based algebraic int. 20100604 tpd src/axiom-website/patches.html 20100604.03.tpd.patch 20100604 tpd src/input/Makefile add rule-based rational integration tests 20100604 tpd src/input/richrational.input add rule-based rational integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index e50b357..4b17456 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2840,5 +2840,7 @@ books/bookvolbib add ES10 Burcin and Stein Axiom reference
books/bookvol10.5 tighten array type declarations
20100605.03.tpd.patch src/input/richrational.input add rule-based rational integration
+20100605.04.tpd.patch +src/input/richalgebraic000-099.input rule-based algebraic integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 105b083..b76e4b1 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -368,7 +368,8 @@ REGRES= ackermann.regress \ quat1.regress quat.regress r20abugs.regress r20bugs.regress \ r21bugsbig.regress r21bugs.regress radff.regress radix.regress \ realclos.regress reclos.regress reclos2.regress regset.regress \ - repa6.regress richrational.regress robidoux.regress \ + repa6.regress richalgebraic000-099.regress \ + richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ schaum1.regress schaum2.regress schaum3.regress schaum4.regress \ @@ -680,6 +681,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/r21bugs.input \ ${OUT}/radff.input ${OUT}/radix.input ${OUT}/realclos.input \ ${OUT}/reclos.input ${OUT}/reclos2.input ${OUT}/regset.input \ + ${OUT}/richalgebraic000-099.input \ ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ @@ -1021,7 +1023,9 @@ DOCFILES= \ ${DOC}/regset.input.dvi ${DOC}/reductio.input.dvi \ ${DOC}/regset.input.dvi ${DOC}/repa6.input.dvi \ ${DOC}/ribbon.input.dvi ${DOC}/ribbons.input.dvi \ - ${DOC}/ribbonsnew.input.dvi ${DOC}/richrational.input.dvi \ + ${DOC}/ribbonsnew.input.dvi \ + ${DOC}/richalgebraic000-099.input.dvi \ + ${DOC}/richrational.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ ${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \ diff --git a/src/input/richalgebraic000-099.input.pamphlet b/src/input/richalgebraic000-099.input.pamphlet new file mode 100644 index 0000000..4913435 --- /dev/null +++ b/src/input/richalgebraic000-099.input.pamphlet @@ -0,0 +1,4982 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richalgebraic000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic000-099.output +)spool richalgebraic000-099.output +)set message test on +)set message auto off +)clear all + +--S 1 of 518 +t0000:= (c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression Integer +--E 1 + +--S 2 of 518 +r0000:= 1/6*(a+b*x)*(c*(a+b*x)^2)^(5/2)/b +--R +--R +--R (2) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R / +--R 6b +--R Type: Expression Integer +--E 2 + +--S 3 of 518 +a0000:= integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 6 4 2 5 2 3 2 4 3 2 2 3 4 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a c x)\|c +--R ------------------------------------------------------------------------ +--R 6 +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 518 +m0000:= a0000-r0000 +--R +--R +--R (4) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (- b c x - 5a b c x - 10a b c x - 10a b c x - 5a b c x - a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x)\|c +--R / +--R 6b +--R Type: Expression Integer +--E 4 + +--S 5 of 518 +d0000:= D(m0000,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +-+ +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 4 2 3 2 5 3 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x - 6a b c x +--R + +--R 6 3 +--R - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression Integer +--E 5 + +--S 6 of 518 +t0001:= (c*(a+b*x)^2)^(3/2) +--R +--R +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (6) (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression Integer +--E 6 + +--S 7 of 518 +r0001:= 1/4*(a+b*x)*(c*(a+b*x)^2)^(3/2)/b +--R +--R +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 2a b c x + a c +--R (7) --------------------------------------------------------------- +--R 4b +--R Type: Expression Integer +--E 7 + +--S 8 of 518 +a0001:= integrate(t0001,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a c x)\|c +--R (8) --------------------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 518 +m0001:= a0001-r0001 +--R +--R +--R (9) +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + 2a b c x + a c +--R + +--R 4 4 3 3 2 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x)\|c +--R / +--R 4b +--R Type: Expression Integer +--E 9 + +--S 10 of 518 +d0001:= D(m0001,x) +--R +--R +--R (10) +--R +-----------------------+ +--R 3 3 2 2 2 3 +-+ | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|c \|b c x + 2a b c x + a c +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression Integer +--E 10 + +--S 11 of 518 +t0002:= 1/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (11) ---------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 11 + +--S 12 of 518 +r0002:= 1/4*(a+b*x)/b/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (12) ---------------------------- +--R +------------------+ +--R | c +--R 4b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 12 + +--S 13 of 518 +a0002:= integrate(t0002,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R b x + 4a b x + 6a b x + 4a x +--R (13) ------------------------------- +--R +-+ +--R 4c\|c +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 518 +m0002:= a0002-r0002 +--R +--R +--R (14) +--R 3 3 2 2 2 3 +-+ +--R (- b x - 3a b x - 3a b x - a )\|c +--R + +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | c +--R (b x + 4a b x + 6a b x + 4a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R | c +-+ +--R 4b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 14 + +--S 15 of 518 +d0002:= D(m0002,x) +--R +--R +--R (15) +--R +------------------+ +--R 3 3 2 2 2 3 | c +-+ 2 2 +--R (b x + 3a b x + 3a b x + a ) |------------------ \|c - b c x +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 +--R - 2a b c x - a c +--R / +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 15 + +--S 16 of 518 +t0003:= 1/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (16) -------------------------------------- +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 16 + +--S 17 of 518 +r0003:= 1/6*(a+b*x)/b/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (17) -------------------------------------------------- +--R +------------------+ +--R 2 | c +--R 6b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 17 + +--S 18 of 518 +a0003:= integrate(t0003,x) +--R +--R +--R 5 6 4 5 2 3 4 3 2 3 4 2 5 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a x +--R (18) ------------------------------------------------------ +--R 2 +-+ +--R 6c \|c +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 518 +m0003:= a0003-r0003 +--R +--R +--R (19) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|c +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x) +--R * +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R 2 | c +-+ +--R 6b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 19 + +--S 20 of 518 +d0003:= D(m0003,x) +--R +--R +--R (20) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a ) +--R * +--R +------------------+ +--R | c +-+ +--R |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +------------------+ +--R 3 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression Integer +--E 20 + +--S 21 of 518 +t0004:= 1/(2-3*x)^(1/2)/(2+3*x)^(1/2) +--R +--R +--R 1 +--R (21) -------------------- +--R +--------+ +------+ +--R \|- 3x + 2 \|3x + 2 +--R Type: Expression Integer +--E 21 + +--S 22 of 518 +r0004:= 1/3*asin(3/2*x) +--R +--R +--R 3x +--R asin(--) +--R 2 +--R (22) -------- +--R 3 +--R Type: Expression Integer +--E 22 + +--S 23 of 518 +--a0004:= integrate(t0004,x) +-- bug 7207: causes infinite loop in integrator. +--E 23 + +--S 24 of 518 +t0005:= 1/(3-x)^(1/2)/(5+x)^(1/2) +--R +--R +--R 1 +--R (23) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x + 5 +--R Type: Expression Integer +--E 24 + +--S 25 of 518 +r0005:= asin(1/4+1/4*x) +--R +--R +--R x + 1 +--R (24) asin(-----) +--R 4 +--R Type: Expression Integer +--E 25 + +--S 26 of 518 +--a0005:= integrate(t0005,x) +--E 26 + +--S 27 of 518 +--m0005:= a0005-r0005 +--E 28 + +--S 28 of 518 +--d0005:= D(m0005,x) +--E 28 + +--S 29 of 518 +t0006:= 1/(-3-x)^(1/2)/(5+x)^(1/2) +--R +--R +--R 1 +--R (25) ------------------ +--R +-------+ +-----+ +--R \|- x - 3 \|x + 5 +--R Type: Expression Integer +--E 29 + +--S 30 of 518 +r0006:= asin(4+x) +--R +--R +--R (26) asin(x + 4) +--R Type: Expression Integer +--E 30 + +--S 31 of 518 +--a0006:= integrate(t0006,x) +--E 31 + +--S 32 of 518 +--m0006:= a0006-r0006 +--E 32 + +--S 33 of 518 +--d0006:= D(m0006,x) +--E 33 + +--S 34 of 518 +t0007:= (1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (27) \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 34 + +--S 35 of 518 +r0007:= 1/2*x*(1-x^2)^(1/2)+1/2*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R x\|- x + 1 + asin(x) +--R (28) ---------------------- +--R 2 +--R Type: Expression Integer +--E 35 + +--S 36 of 518 +--a0007:= integrate(t0007,x) +--E 36 + +--S 37 of 518 +--m0007:= a0007-r0007 +--E 37 + +--S 38 of 518 +--d0007:= D(m0007,x) +--E 38 + +--S 39 of 518 +t0008:= 1/(1-x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 1 +--R (29) ------------------ +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 39 + +--S 40 of 518 +r0008:= asin(x) +--R +--R +--R (30) asin(x) +--R Type: Expression Integer +--E 40 + +--S 41 of 518 +--a0008:= integrate(t0008,x) +--E 41 + +--S 42 of 518 +--m0008:= a0008-r0008 +--E 42 + +--S 43 of 518 +--d0008:= D(m0008,x) +--E 43 + +--S 44 of 518 +t0009:= 1/(1-x)^(3/2)/(1+x)^(3/2) +--R +--R +--R 1 +--R (31) - -------------------------- +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 44 + +--S 45 of 518 +r0009:= x/(1-x^2)^(1/2) +--R +--R +--R x +--R (32) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression Integer +--E 45 + +\end{chunk} +Occasionally we get a different answer to this same integration: +\begin{verbatim} + + + +-------+ +-----+ + x\|- x + 1 \|x + 1 + (33) - ------------------- + 2 + x - 1 + Type: Union(Expression Integer,...) +\end{verbatim} +Both answers are correct as can be seen by taking the difference between +the original integrand and the derivative of the expression. +\begin{chunk}{*} +--S 46 of 518 +a0009:= integrate(t0009,x) +--R +--R +--R +-------+ +-----+ 2 +--R - 3x\|- x + 1 \|x + 1 - 2x + 2 +--R (33) -------------------------------- +--R 2 +--R 3x - 3 +--R Type: Union(Expression Integer,...) +--E 46 + +\end{chunk} +Occasionally we get a different answer to this same integration: +\begin{verbatim} + + + +--------+ + | 2 +-------+ +-----+ 3 + - x\|- x + 1 \|- x + 1 \|x + 1 - x + x + (34) ----------------------------------------- + +--------+ + 2 | 2 + (x - 1)\|- x + 1 + Type: Expression Integer +\end{verbatim} +Both answers are correct as can be seen by taking the difference between +the original integrand and the derivative of the expression. +\begin{chunk}{*} +--S 47 of 518 +m0009:= a0009-r0009 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ 2 | 2 3 +--R - 3x\|- x + 1 \|- x + 1 \|x + 1 + (- 2x + 2)\|- x + 1 - 3x + 3x +--R (34) --------------------------------------------------------------------- +--R +--------+ +--R 2 | 2 +--R (3x - 3)\|- x + 1 +--R Type: Expression Integer +--E 47 + +--S 48 of 518 +d0009:= D(m0009,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- x + 1 \|x + 1 - \|- x + 1 +--R (35) ------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 48 + +--S 49 of 518 +t0010:= (3-x)^(1/2)*(-2+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (36) \|- x + 3 \|x - 2 +--R Type: Expression Integer +--E 49 + +--S 50 of 518 +r0010:= -1/4*(5-2*x)*(-6+5*x-x^2)^(1/2)+1/8*asin(-5+2*x) +--R +--R +--R +-------------+ +--R | 2 +--R (4x - 10)\|- x + 5x - 6 + asin(2x - 5) +--R (37) ---------------------------------------- +--R 8 +--R Type: Expression Integer +--E 50 + +--S 51 of 518 +--a0010:= integrate(t0010,x) +--E 51 + +--S 52 of 518 +--m0010:= a0010-r0010 +--E 52 + +--S 53 of 518 +--d0010:= D(m0010,x) +--E 53 + +--S 54 of 518 +t0011:= 1/(3-x)^(1/2)/(-2+x)^(1/2) +--R +--R +--R 1 +--R (38) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x - 2 +--R Type: Expression Integer +--E 54 + +--S 55 of 518 +r0011:= asin(-5+2*x) +--R +--R +--R (39) asin(2x - 5) +--R Type: Expression Integer +--E 55 + +--S 56 of 518 +--a0011:= integrate(t0011,x) +--E 56 + +--S 57 of 518 +--m0011:= a0011-r0011 +--E 57 + +--S 58 of 518 +--d0011:= D(m0011,x) +--E 58 + +--S 59 of 518 +t0012:= x^(1/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (40) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression Integer +--E 59 + +--S 60 of 518 +r0012:= x^(1/2)/b/(a-b*x)-atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(1/2)/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (- b x + a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (41) ----------------------------------------- +--R 2 +-+ +-+ +--R (b x - a b)\|a \|b +--R Type: Expression Integer +--E 60 + +--S 61 of 518 +a0012:= integrate(t0012,x) +--R +--R +--R (42) +--R +-+ +---+ +--R - 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(----------------------------) - 2\|a b \|x +--R b x - a +--R [--------------------------------------------------------, +--R 2 +---+ +--R (2b x - 2a b)\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (- b x + a)atan(------------) - \|- a b \|x +--R a +--R --------------------------------------------] +--R 2 +-----+ +--R (b x - a b)\|- a b +--R Type: Union(List Expression Integer,...) +--E 61 + +--S 62 of 518 +m0012a:= a0012.1-r0012 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (43) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression Integer +--E 62 + +--S 63 of 518 +d0012a:= D(m0012a,x) +--R +--R +--R (44) 0 +--R Type: Expression Integer +--E 63 + +--S 64 of 518 +m0012b:= a0012.1-r0012 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (45) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression Integer +--E 64 + +--S 65 of 518 +d0012b:= D(m0012b,x) +--R +--R +--R (46) 0 +--R Type: Expression Integer +--E 65 + +--S 66 of 518 +t0013:= x^(1/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (47) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression Integer +--E 66 + +--S 67 of 518 +r0013:= -1/2*x^(1/2)/b/(a-b*x)^2+1/4*x^(1/2)/a/b/(a-b*x)+_ + 1/4*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(3/2)/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x - 2a b x + a )atanh(--------) + (- b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (48) ------------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x - 8a b x + 4a b)\|a \|b +--R Type: Expression Integer +--E 67 + +--S 68 of 518 +a0013:= integrate(t0013,x) +--R +--R +--R (49) +--R [ +--R +-+ +---+ +--R 2 2 2 2a b\|x + (b x + a)\|a b +--R (b x - 2a b x + a )log(--------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 2b x - 2a)\|a b \|x +--R / +--R 3 2 2 2 3 +---+ +--R (8a b x - 16a b x + 8a b)\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (b x - 2a b x + a )atan(------------) + (- b x - a)\|- a b \|x +--R a +--R ----------------------------------------------------------------] +--R 3 2 2 2 3 +-----+ +--R (4a b x - 8a b x + 4a b)\|- a b +--R Type: Union(List Expression Integer,...) +--E 68 + +--S 69 of 518 +m0013a:= a0013.1-r0013 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (50) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression Integer +--E 69 + +--S 70 of 518 +d0013a:= D(m0013a,x) +--R +--R +--R (51) 0 +--R Type: Expression Integer +--E 70 + +--S 71 of 518 +m0013b:= a0013.2-r0013 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (52) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R 4a b\|- a b \|a \|b +--R Type: Expression Integer +--E 71 + +--S 72 of 518 +d0013b:= D(m0013b,x) +--R +--R +--R (53) 0 +--R Type: Expression Integer +--E 72 + +--S 73 of 518 +t0014:= x^(3/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (54) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression Integer +--E 73 + +--S 74 of 518 +r0014:= 3*x^(1/2)/b^2+x^(3/2)/b/(a-b*x)-_ + 3*a^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x + 3a)\|a atanh(--------) + (2b x - 3a)\|b \|x +--R +-+ +--R \|a +--R (55) ------------------------------------------------------ +--R 3 2 +-+ +--R (b x - a b )\|b +--R Type: Expression Integer +--E 74 + +--S 75 of 518 +a0014:= integrate(t0014,x) +--R +--R +--R (56) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R (3b x - 3a) |- log(----------------------) + (4b x - 6a)\|x +--R \|b b x - a +--R [------------------------------------------------------------, +--R 3 2 +--R 2b x - 2a b +--R +---+ +-+ +--R | a \|x +-+ +--R (- 3b x + 3a) |- - atan(------) + (2b x - 3a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------] +--R 3 2 +--R b x - a b +--R Type: Union(List Expression Integer,...) +--E 75 + +--S 76 of 518 +m0014a:= a0014.1-r0014 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 3 |- \|b log(---------------------- + 6\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (57) ----------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression Integer +--E 76 + +--S 77 of 518 +d0014a:= D(m0014a,x) +--R +--R +--R (58) 0 +--R Type: Expression Integer +--E 77 + +--S 78 of 518 +m0014b:= a0014.2-r0014 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 3\|a atanh(--------) - 3 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (59) ---------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression Integer +--E 78 + +--S 79 of 518 +d0014b:= D(m0014b,x) +--R +--R +--R (60) 0 +--R Type: Expression Integer +--E 79 + +--S 80 of 518 +t0015:= x^(3/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (61) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression Integer +--E 80 + +--S 81 of 518 +r0015:= -1/2*x^(3/2)/b/(a-b*x)^2+_ + 3/4*x^(1/2)/b^2/(a-b*x)-_ + 3/4*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(1/2)/b^(5/2) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (- 5b x + 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (62) ------------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x - 8a b x + 4a b )\|a \|b +--R Type: Expression Integer +--E 81 + +--S 82 of 518 +a0015:= integrate(t0015,x) +--R +--R +--R (63) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 10b x + 6a)\|a b \|x +--R / +--R 4 2 3 2 2 +---+ +--R (8b x - 16a b x + 8a b )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (- 5b x + 3a)\|- a b \|x +--R a +--R ----------------------------------------------------------------------] +--R 4 2 3 2 2 +-----+ +--R (4b x - 8a b x + 4a b )\|- a b +--R Type: Union(List Expression Integer,...) +--E 82 + +--S 83 of 518 +m0015a:= a0015.1-r0015 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (64) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression Integer +--E 83 + +--S 84 of 518 +d0015a:= D(m0015a,x) +--R +--R +--R (65) 0 +--R Type: Expression Integer +--E 84 + +--S 85 of 518 +m0015b:= a0015.2-r0015 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (66) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4b \|- a b \|a \|b +--R Type: Expression Integer +--E 85 + +--S 86 of 518 +d0015b:= D(m0015b,x) +--R +--R +--R (67) 0 +--R Type: Expression Integer +--E 86 + +--S 87 of 518 +t0016:= x^(5/2)/(-a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (68) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression Integer +--E 87 + +--S 88 of 518 +r0016:= 5*a*x^(1/2)/b^3+5/3*x^(3/2)/b^2+x^(5/2)/b/(a-b*x)-_ + 5*a^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(7/2) +--R +--R +--R (69) +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (- 15a b x + 15a )\|a atanh(--------) + (2b x + 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 4 3 +-+ +--R (3b x - 3a b )\|b +--R Type: Expression Integer +--E 88 + +--S 89 of 518 +a0016:= integrate(t0016,x) +--R +--R +--R (70) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b +--R (15a b x - 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (4b x + 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x - 6a b +--R , +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R (- 15a b x + 15a ) |- - atan(------) + (2b x + 10a b x - 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------------------] +--R 4 3 +--R 3b x - 3a b +--R Type: Union(List Expression Integer,...) +--E 89 + +--S 90 of 518 +m0016a:= a0016.1-r0016 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 5a |- \|b log(----------------------) + 10a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (71) -------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression Integer +--E 90 + +--S 91 of 518 +d0016a:= D(m0016a,x) +--R +--R +--R (72) 0 +--R Type: Expression Integer +--E 91 + +--S 92 of 518 +m0016b:= a0016.2-r0016 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 5a\|a atanh(--------) - 5a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (73) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression Integer +--E 92 + +--S 93 of 518 +d0016b:= D(m0016b,x) +--R +--R +--R (74) 0 +--R Type: Expression Integer +--E 93 + +--S 94 of 518 +t0017:= x^(5/2)/(-a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (75) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression Integer +--E 94 + +--S 95 of 518 +r0017:= 15/4*x^(1/2)/b^3-1/2*x^(5/2)/b/(a-b*x)^2+_ + 5/4*x^(3/2)/b^2/(a-b*x)-_ + 15/4*a^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(7/2) +--R +--R +--R (76) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x - 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x - 8a b x + 4a b )\|b +--R Type: Expression Integer +--E 95 + +--S 96 of 518 +a0017:= integrate(t0017,x) +--R +--R +--R (77) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 |a \|b +--R (15b x - 30a b x + 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (16b x - 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x - 16a b x + 8a b +--R , +--R +---+ +-+ +--R 2 2 2 | a \|x 2 2 2 +-+ +--R (- 15b x + 30a b x - 15a ) |- - atan(------) + (8b x - 25a b x + 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ---------------------------------------------------------------------------- +--R 5 2 4 2 3 +--R 4b x - 8a b x + 4a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 96 + +--S 97 of 518 +m0017a:= a0017.1-r0017 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 15 |- \|b log(---------------------- + 30\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (78) ------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression Integer +--E 97 + +--S 98 of 518 +d0017a:= D(m0017a,x) +--R +--R +--R (79) 0 +--R Type: Expression Integer +--E 98 + +--S 99 of 518 +m0017b:= a0017.2-r0017 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 15\|a atanh(--------) - 15 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (80) ------------------------------------------------ +--R 3 +-+ +--R 4b \|b +--R Type: Expression Integer +--E 99 + +--S 100 of 518 +d0017b:= D(m0017b,x) +--R +--R +--R (81) 0 +--R Type: Expression Integer +--E 100 + +--S 101 of 518 +t0018:= 1/x^(3/2)/(-a+b*x)^2 +--R +--R +--R 1 +--R (82) -------------------------- +--R 2 3 2 2 +-+ +--R (b x - 2a b x + a x)\|x +--R Type: Expression Integer +--E 101 + +--S 102 of 518 +r0018:= -2/a/x^(1/2)/(a-b*x)+3*b*x^(1/2)/a^2/(a-b*x)+_ + 3*b^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (3b x - 3a)\|b \|x atanh(--------) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (83) ------------------------------------------------------ +--R 2 3 +-+ +-+ +--R (a b x - a )\|a \|x +--R Type: Expression Integer +--E 102 + +--S 103 of 518 +a0018:= integrate(t0018,x) +--R +--R +--R (84) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R |b +-+ \|a +--R (3b x - 3a) |- \|x log(--------------------) - 6b x + 4a +--R \|a b x - a +--R [--------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x - 2a )\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R (3b x - 3a) |- - \|x atan(-------) - 3b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ----------------------------------------------] +--R 2 3 +-+ +--R (a b x - a )\|x +--R Type: Union(List Expression Integer,...) +--E 103 + +--S 104 of 518 +m0018a:= a0018.1-r0018 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 3\|a |- log(--------------------) - 6\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (85) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression Integer +--E 104 + +--S 105 of 518 +d0018a:= D(m0018a,x) +--R +--R +--R (86) 0 +--R Type: Expression Integer +--E 105 + +--S 106 of 518 +m0018b:= a0018.2-r0018 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 3\|b atanh(--------) + 3 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (87) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression Integer +--E 106 + +--S 107 of 518 +d0018b:= D(m0018b,x) +--R +--R +--R (88) 0 +--R Type: Expression Integer +--E 107 + +--S 108 of 518 +t0019:= 1/x^(3/2)/(-a+b*x)^3 +--R +--R +--R 1 +--R (89) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a x)\|x +--R Type: Expression Integer +--E 108 + +--S 109 of 518 +r0019:= 2/a/x^(1/2)/(a-b*x)^2-5/2*b*x^(1/2)/a^2/(a-b*x)^2-_ + 15/4*b*x^(1/2)/a^3/(a-b*x)-_ + 15/4*b^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (90) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (15b x - 25a b x + 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|x +--R Type: Expression Integer +--E 109 + +--S 110 of 518 +a0019:= integrate(t0019,x) +--R +--R +--R (91) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 2 |b +-+ \|a 2 2 +--R (15b x - 30a b x + 15a ) |- \|x log(----------------------) + 30b x +--R \|a b x - a +--R + +--R 2 +--R - 50a b x + 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x - 16a b x + 8a )\|x +--R , +--R +---+ +-+ +--R 2 2 2 | b +-+ b\|x 2 2 2 +--R (- 15b x + 30a b x - 15a ) |- - \|x atan(-------) + 15b x - 25a b x + 8a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ---------------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x - 8a b x + 4a )\|x +--R Type: Union(List Expression Integer,...) +--E 110 + +--S 111 of 518 +m0019a:= a0019.1-r0019 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 15\|a |- log(----------------------) + 30\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (92) ------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 111 + +--S 112 of 518 +d0019a:= D(m0019a,x) +--R +--R +--R (93) 0 +--R Type: Expression Integer +--E 112 + +--S 113 of 518 +m0019b:= a0019.2-r0019 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 15\|b atanh(--------) - 15 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (94) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression Integer +--E 113 + +--S 114 of 518 +d0019b:= D(m0019b,x) +--R +--R +--R (95) 0 +--R Type: Expression Integer +--E 114 + +--S 115 of 518 +t0020:= 1/x^(5/2)/(-a+b*x)^2 +--R +--R +--R 1 +--R (96) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x - 2a b x + a x )\|x +--R Type: Expression Integer +--E 115 + +--S 116 of 518 +r0020:= -5/3/a^2/x^(3/2)-5*b/a^3/x^(1/2)+1/a/x^(3/2)/(a-b*x)+_ + 5*b^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (97) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x - 15a b x)\|b \|x atanh(--------) + (- 15b x + 10a b x + 2a )\|a +--R +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x - 3a x)\|a \|x +--R Type: Expression Integer +--E 116 + +--S 117 of 518 +a0020:= integrate(t0020,x) +--R +--R +--R (98) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R (15b x - 15a b x) |- \|x log(--------------------) - 30b x + 20a b x + 4a +--R \|a b x - a +--R [---------------------------------------------------------------------------- +--R 3 2 4 +-+ +--R (6a b x - 6a x)\|x +--R , +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R (15b x - 15a b x) |- - \|x atan(-------) - 15b x + 10a b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ------------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x - 3a x)\|x +--R Type: Union(List Expression Integer,...) +--E 117 + +--S 118 of 518 +m0020a:= a0020.1-r0020 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 5b\|a |- log(--------------------) - 10b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (99) ------------------------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression Integer +--E 118 + +--S 119 of 518 +d0020a:= D(m0020a,x) +--R +--R +--R (100) 0 +--R Type: Expression Integer +--E 119 + +--S 120 of 518 +m0020b:= a0020.2-r0020 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 5b\|b atanh(--------) + 5b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (101) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression Integer +--E 120 + +--S 121 of 518 +d0020b:= D(m0020b,x) +--R +--R +--R (102) 0 +--R Type: Expression Integer +--E 121 + +--S 122 of 518 +t0021:= 1/x^(5/2)/(-a+b*x)^3 +--R +--R +--R 1 +--R (103) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x - 3a b x + 3a b x - a x )\|x +--R Type: Expression Integer +--E 122 + +--S 123 of 518 +r0021:= 2/3/a/x^(3/2)/(a-b*x)^2+14/3*b/a^2/x^(1/2)/(a-b*x)^2-_ + 35/6*b^2*x^(1/2)/a^3/(a-b*x)^2-35/4*b^2*x^(1/2)/a^4/(a-b*x)-_ + 35/4*b^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (104) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (- 105b x + 210a b x - 105a b x)\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 175a b x + 56a b x + 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x - 24a b x + 12a x)\|a \|x +--R Type: Expression Integer +--E 123 + +--S 124 of 518 +a0021:= integrate(t0021,x) +--R +--R +--R (105) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 3 3 2 2 2 |b +-+ \|a +--R (105b x - 210a b x + 105a b x) |- \|x log(----------------------) +--R \|a b x - a +--R + +--R 3 3 2 2 2 3 +--R 210b x - 350a b x + 112a b x + 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x - 48a b x + 24a x)\|x +--R , +--R +--R +---+ +-+ +--R 3 3 2 2 2 | b +-+ b\|x 3 3 +--R (- 105b x + 210a b x - 105a b x) |- - \|x atan(-------) + 105b x +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R + +--R 2 2 2 3 +--R - 175a b x + 56a b x + 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x - 24a b x + 12a x)\|x +--R ] +--R Type: Union(List Expression Integer,...) +--E 124 + +--S 125 of 518 +m0021a:= a0021.1-r0021 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 35b\|a |- log(----------------------) + 70b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (106) --------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 125 + +--S 126 of 518 +d0021a:= D(m0021a,x) +--R +--R +--R (107) 0 +--R Type: Expression Integer +--E 126 + +--S 127 of 518 +m0021b:= a0021.2-r0021 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 35b\|b atanh(--------) - 35b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (108) --------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression Integer +--E 127 + +--S 128 of 518 +d0021b:= D(m0021b,x) +--R +--R +--R (109) 0 +--R Type: Expression Integer +--E 128 + +--S 129 of 518 +t0022:= x^(1/2)*(2+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (110) \|x \|b x + 2 +--R Type: Expression Integer +--E 129 + +--S 130 of 518 +r0022:= 1/2*x^(1/2)*(2+b*x)^(1/2)/b+1/2*x^(3/2)*(2+b*x)^(1/2)-_ + asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R - 2asinh(------------) + (b x + 1)\|b \|x \|b x + 2 +--R 2 +--R (111) ---------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression Integer +--E 130 + +--S 131 of 518 +--a0022:= integrate(t0022,x) +--E 131 + +--S 132 of 518 +--m0022:= a0022-r0022 +--E 132 + +--S 133 of 518 +--d0022:= D(m0022,x) +--E 133 + +--S 134 of 518 +t0023:= x^(1/2)/(2+b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (112) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression Integer +--E 134 + +--S 135 of 518 +r0023:= x^(1/2)*(2+b*x)^(1/2)/b-2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R - 2asinh(------------) + \|b \|x \|b x + 2 +--R 2 +--R (113) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression Integer +--E 135 + +--S 136 of 518 +--a0023:= integrate(t0023,x) +--E 136 + +--S 137 of 518 +--m0023:= a0023-r0023 +--E 137 + +--S 138 of 518 +--d0023:= D(m0023,x) +--E 138 + +--S 139 of 518 +t0024:= x^(3/2)/(2+b*x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (114) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression Integer +--E 139 + +--S 140 of 518 +r0024:= -3/2*x^(1/2)*(2+b*x)^(1/2)/b^2+1/2*x^(3/2)*(2+b*x)^(1/2)/b+_ + 3*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 6asinh(------------) + (b x - 3)\|b \|x \|b x + 2 +--R 2 +--R (115) -------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression Integer +--E 140 + +--S 141 of 518 +--a0024:= integrate(t0024,x) +--E 141 + +--S 142 of 518 +--m0024:= a0024-r0024 +--E 142 + +--S 143 of 518 +--d0024:= D(m0024,x) +--E 143 + +--S 144 of 518 +t0025:= x^(3/2)/(2+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (116) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression Integer +--E 144 + +--S 145 of 518 +r0025:= -2*x^(3/2)/b/(2+b*x)^(1/2)+3*x^(1/2)*(2+b*x)^(1/2)/b^2-_ + 6*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x +-+ +-+ +--R - 6\|b x + 2 asinh(------------) + (b x + 6)\|b \|x +--R 2 +--R (117) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + 2 +--R Type: Expression Integer +--E 145 + +--S 146 of 518 +--a0025:= integrate(t0025,x) +--E 146 + +--S 147 of 518 +--m0025:= a0025-r0025 +--E 147 + +--S 148 of 518 +--d0025:= D(m0025,x) +--E 148 + +--S 149 of 518 +t0026:= x^(5/2)/(2+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (118) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression Integer +--E 149 + +--S 150 of 518 +r0026:= 1/2/b^(7/2)*(x^(5/2)*b^(5/2)-30*x^(1/2)*b^(1/2)-5*x^(3/2)*b^(3/2)+_ + 30*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))*(2+b*x)^(1/2))/(2+b*x)^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x 2 2 +-+ +-+ +--R 30\|b x + 2 asinh(------------) + (b x - 5b x - 30)\|b \|x +--R 2 +--R (119) ------------------------------------------------------------ +--R 3 +-+ +-------+ +--R 2b \|b \|b x + 2 +--R Type: Expression Integer +--E 150 + +--S 151 of 518 +--a0026:= integrate(t0026,x) +--E 151 + +--S 152 of 518 +--m0026:= a0026-r0026 +--E 152 + +--S 153 of 518 +--d0026:= D(m0026,x) +--E 153 + +--S 154 of 518 +t0027:= x^(5/2)/(2+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (120) --------------------------- +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R Type: Expression Integer +--E 154 + +--S 155 of 518 +r0027:= -2/3*x^(5/2)/b/(2+b*x)^(3/2)-10/3*x^(3/2)/b^2/(2+b*x)^(1/2)+_ + 5*x^(1/2)*(2+b*x)^(1/2)/b^3-_ + 10*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(7/2) +--R +--R +--R (121) +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x 2 2 +-+ +-+ +--R (- 30b x - 60)\|b x + 2 asinh(------------) + (3b x + 40b x + 60)\|b \|x +--R 2 +--R -------------------------------------------------------------------------- +--R 4 3 +-+ +-------+ +--R (3b x + 6b )\|b \|b x + 2 +--R Type: Expression Integer +--E 155 + +--S 156 of 518 +--a0027:= integrate(t0027,x) +--E 156 + +--S 157 of 518 +--m0027:= a0027-r0027 +--E 157 + +--S 158 of 518 +--d0027:= D(m0027,x) +--E 158 + +--S 159 of 518 +t0028:= (2+b*x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (122) ---------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 159 + +--S 160 of 518 +r0028:= x^(1/2)*(2+b*x)^(1/2)+2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 2asinh(------------) + \|b \|x \|b x + 2 +--R 2 +--R (123) ----------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 160 + +--S 161 of 518 +--a0028:= integrate(t0028,x) +--E 161 + +--S 162 of 518 +--m0028:= a0028-r0028 +--E 162 + +--S 163 of 518 +--d0028:= D(m0028,x) +--E 163 + +--S 164 of 518 +t0029:= (2+b*x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (124) ------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 164 + +--S 165 of 518 +r0029:= 3/2*x^(1/2)*(2+b*x)^(1/2)+1/2*x^(1/2)*(2+b*x)^(3/2)+_ + 3*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 6asinh(------------) + (b x + 5)\|b \|x \|b x + 2 +--R 2 +--R (125) -------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 165 + +--S 166 of 518 +--a0029:= integrate(t0029,x) +--E 166 + +--S 167 of 518 +--m0029:= a0029-r0029 +--E 167 + +--S 168 of 518 +--d0029:= D(m0029,x) +--E 168 + +--S 169 of 518 +t0030:= 1/x^(1/2)/(2+b*x)^(1/2) +--R +--R +--R 1 +--R (126) -------------- +--R +-+ +-------+ +--R \|x \|b x + 2 +--R Type: Expression Integer +--E 169 + +--S 170 of 518 +r0030:= 2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +--R 2asinh(------------) +--R 2 +--R (127) -------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 170 + +--S 171 of 518 +--a0030:= integrate(t0030,x) +--E 171 + +--S 172 of 518 +--m0030:= a0030-r0030 +--E 172 + +--S 173 of 518 +--d0030:= D(m0030,x) +--E 173 + +--S 174 of 518 +t0031:= (2+b*x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (128) ---------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 174 + +--S 175 of 518 +r0031:= -2*(2+b*x)^(1/2)/x^(1/2)+2*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 2\|b \|x asinh(------------) - 2\|b x + 2 +--R 2 +--R (129) ------------------------------------------ +--R +-+ +--R \|x +--R Type: Expression Integer +--E 175 + +--S 176 of 518 +--a0031:= integrate(t0031,x) +--E 176 + +--S 177 of 518 +--m0031:= a0031-r0031 +--E 177 + +--S 178 of 518 +--d0031:= D(m0031,x) +--E 178 + +--S 179 of 518 +t0032:= (2+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (130) ------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 179 + +--S 180 of 518 +r0032:= 3*b*x^(1/2)*(2+b*x)^(1/2)-2*(2+b*x)^(3/2)/x^(1/2)+_ + 6*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 6\|b \|x asinh(------------) + (b x - 4)\|b x + 2 +--R 2 +--R (131) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 180 + +--S 181 of 518 +--a0032:= integrate(t0032,x) +--E 181 + +--S 182 of 518 +--m0032:= a0032-r0032 +--E 182 + +--S 183 of 518 +--d0032:= D(m0032,x) +--E 183 + +--S 184 of 518 +t0033:= (2+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (132) --------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 184 + +--S 185 of 518 +r0033:= 15/2*b*x^(1/2)*(2+b*x)^(1/2)+5/2*b*x^(1/2)*(2+b*x)^(3/2)-_ + 2*(2+b*x)^(5/2)/x^(1/2)+15*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +-------+ +--R 30\|b \|x asinh(------------) + (b x + 9b x - 16)\|b x + 2 +--R 2 +--R (133) ------------------------------------------------------------ +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 185 + +--S 186 of 518 +--a0033:= integrate(t0033,x) +--E 186 + +--S 187 of 518 +--m0033:= a0033-r0033 +--E 187 + +--S 188 of 518 +--d0033:= D(m0033,x) +--E 188 + +--S 189 of 518 +t0034:= (2+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (134) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 189 + +--S 190 of 518 +r0034:= -2*b*(2+b*x)^(1/2)/x^(1/2)-2/3*(2+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 6b x\|b \|x asinh(------------) + (- 8b x - 4)\|b x + 2 +--R 2 +--R (135) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 190 + +--S 191 of 518 +--a0034:= integrate(t0034,x) +--E 191 + +--S 192 of 518 +--m0034:= a0034-r0034 +--E 192 + +--S 193 of 518 +--d0034:= D(m0034,x) +--E 193 + +--S 194 of 518 +t0035:= (2+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (136) --------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 194 + +--S 195 of 518 +r0035:= 1/3*(3*b^2*x^2*(2+b*x)^(1/2)-28*b*x*(2+b*x)^(1/2)-8*(2+b*x)^(1/2)+_ + 30*b^(3/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))*x^(3/2))/x^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +-------+ +--R 30b x\|b \|x asinh(------------) + (3b x - 28b x - 8)\|b x + 2 +--R 2 +--R (137) ---------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 195 + +--S 196 of 518 +--a0035:= integrate(t0035,x) +--E 196 + +--S 197 of 518 +--m0035:= a0035-r0035 +--E 197 + +--S 198 of 518 +--d0035:= D(m0035,x) +--E 198 + +--S 199 of 518 +t0036:= x^(1/2)*(a+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (138) \|x \|b x + a +--R Type: Expression Integer +--E 199 + +--S 200 of 518 +r0036:= 1/4*a*x^(1/2)*(a+b*x)^(1/2)/b+1/2*x^(3/2)*(a+b*x)^(1/2)-_ + 1/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + (2b x + a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (139) ---------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression Integer +--E 200 + +--S 201 of 518 +--a0036:= integrate(t0036,x) +--E 201 + +--S 202 of 518 +--m0036:= a0036-r0036 +--E 202 + +--S 203 of 518 +--d0036:= D(m0036,x) +--E 203 + +--S 204 of 518 +t0037:= x^(1/2)*(a+b*x)^(3/2) +--R +--R +--R +-+ +-------+ +--R (140) (b x + a)\|x \|b x + a +--R Type: Expression Integer +--E 204 + +--S 205 of 518 +r0037:= -1/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b-1/12*a*x^(1/2)*(a+b*x)^(3/2)/b+_ + 1/3*x^(1/2)*(a+b*x)^(5/2)/b-_ + 1/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 3a atanh(----------) + (8b x + 14a b x + 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (141) ------------------------------------------------------------------ +--R +-+ +--R 24b\|b +--R Type: Expression Integer +--E 205 + +--S 206 of 518 +--a0037:= integrate(t0037,x) +--E 206 + +--S 207 of 518 +--m0037:= a0037-r0037 +--E 207 + +--S 208 of 518 +--d0037:= D(m0037,x) +--E 208 + +--S 209 of 518 +t0038:= x^(1/2)/(a+b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (142) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression Integer +--E 209 + +--S 210 of 518 +r0038:= x^(1/2)*(a+b*x)^(1/2)/b-a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (143) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression Integer +--E 210 + +--S 211 of 518 +--a0038:= integrate(t0038,x) +--E 211 + +--S 212 of 518 +--m0038:= a0038-r0038 +--E 212 + +--S 213 of 518 +--d0038:= D(m0038,x) +--E 213 + +--S 214 of 518 +t0039:= x^(1/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (144) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 214 + +--S 215 of 518 +r0039:= -2*x^(1/2)/b/(a+b*x)^(1/2)+_ + 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R 2\|b x + a atanh(----------) - 2\|b \|x +--R +-------+ +--R \|b x + a +--R (145) ---------------------------------------- +--R +-+ +-------+ +--R b\|b \|b x + a +--R Type: Expression Integer +--E 215 + +--S 216 of 518 +--a0039:= integrate(t0039,x) +--E 216 + +--S 217 of 518 +--m0039:= a0039-r0039 +--E 217 + +--S 218 of 518 +--d0039:= D(m0039,x) +--E 218 + +--S 219 of 518 +t0040:= x^(3/2)*(a+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (146) x\|x \|b x + a +--R Type: Expression Integer +--E 219 + +--S 220 of 518 +r0040:= -1/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b^2+1/12*a*x^(3/2)*(a+b*x)^(1/2)/b+_ + 1/3*x^(5/2)*(a+b*x)^(1/2)+_ + 1/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 3a atanh(----------) + (8b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (147) --------------------------------------------------------------- +--R 2 +-+ +--R 24b \|b +--R Type: Expression Integer +--E 220 + +--S 221 of 518 +--a0040:= integrate(t0040,x) +--E 221 + +--S 222 of 518 +--m0040:= a0040-r0040 +--E 222 + +--S 223 of 518 +--d0040:= D(m0040,x) +--E 223 + +--S 224 of 518 +t0041:= x^(3/2)/(a+b*x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (148) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression Integer +--E 224 + +--S 225 of 518 +r0041:= -3/4*a*x^(1/2)*(a+b*x)^(1/2)/b^2+1/2*x^(3/2)*(a+b*x)^(1/2)/b+_ + 3/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x - 3a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (149) ---------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression Integer +--E 225 + +--S 226 of 518 +--a0041:= integrate(t0041,x) +--E 226 + +--S 227 of 518 +--m0041:= a0041-r0041 +--E 227 + +--S 228 of 518 +--d0041:= D(m0041,x) +--E 228 + +--S 229 of 518 +t0042:= x^(3/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (150) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 229 + +--S 230 of 518 +r0042:= -2*x^(3/2)/b/(a+b*x)^(1/2)+3*x^(1/2)*(a+b*x)^(1/2)/b^2-_ + 3*a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R - 3a\|b x + a atanh(----------) + (b x + 3a)\|b \|x +--R +-------+ +--R \|b x + a +--R (151) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + a +--R Type: Expression Integer +--E 230 + +--S 231 of 518 +--a0042:= integrate(t0042,x) +--E 231 + +--S 232 of 518 +--m0042:= a0042-r0042 +--E 232 + +--S 233 of 518 +--d0042:= D(m0042,x) +--E 233 + +--S 234 of 518 +t0043:= x^(3/2)/(a+b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (152) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 234 + +--S 235 of 518 +r0043:= -2/3*x^(3/2)/b/(a+b*x)^(3/2)-2*x^(1/2)/b^2/(a+b*x)^(1/2)+_ + 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R (6b x + 6a)\|b x + a atanh(----------) + (- 8b x - 6a)\|b \|x +--R +-------+ +--R \|b x + a +--R (153) -------------------------------------------------------------- +--R 3 2 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression Integer +--E 235 + +--S 236 of 518 +--a0043:= integrate(t0043,x) +--E 236 + +--S 237 of 518 +--m0043:= a0043-r0043 +--E 237 + +--S 238 of 518 +--d0043:= D(m0043,x) +--E 238 + +--S 239 of 518 +t0044:= x^(5/2)/(a+b*x)^(1/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (154) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression Integer +--E 239 + +--S 240 of 518 +r0044:= 5/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b^3-5/12*a*x^(3/2)*(a+b*x)^(1/2)/b^2+_ + 1/3*x^(5/2)*(a+b*x)^(1/2)/b-_ + 5/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(7/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 15a atanh(----------) + (8b x - 10a b x + 15a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (155) -------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression Integer +--E 240 + +--S 241 of 518 +--a0044:= integrate(t0044,x) +--E 241 + +--S 242 of 518 +--m0044:= a0044-r0044 +--E 242 + +--S 243 of 518 +--d0044:= D(m0044,x) +--E 243 + +--S 244 of 518 +t0045:= x^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (156) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 244 + +--S 245 of 518 +r0045:= 1/4/b^(7/2)*(2*x^(5/2)*b^(5/2)-15*a^2*x^(1/2)*b^(1/2)-_ + 5*a*x^(3/2)*b^(3/2)+_ + 15*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))*(a+b*x)^(1/2))/_ + (a+b*x)^(1/2) +--R +--R +--R +-+ +-+ +--R 2 +-------+ \|b \|x 2 2 2 +-+ +-+ +--R 15a \|b x + a atanh(----------) + (2b x - 5a b x - 15a )\|b \|x +--R +-------+ +--R \|b x + a +--R (157) ----------------------------------------------------------------- +--R 3 +-+ +-------+ +--R 4b \|b \|b x + a +--R Type: Expression Integer +--E 245 + +--S 246 of 518 +--a0045:= integrate(t0045,x) +--E 246 + +--S 247 of 518 +--m0045:= a0045-r0045 +--E 247 + +--S 248 of 518 +--d0045:= D(m0045,x) +--E 248 + +--S 249 of 518 +t0046:= x^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (158) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 249 + +--S 250 of 518 +r0046:= -2/3*x^(5/2)/b/(a+b*x)^(3/2)-10/3*x^(3/2)/b^2/(a+b*x)^(1/2)+_ + 5*x^(1/2)*(a+b*x)^(1/2)/b^3-_ + 5*a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(7/2) +--R +--R +--R (159) +--R +-+ +-+ +--R 2 +-------+ \|b \|x +--R (- 15a b x - 15a )\|b x + a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x + 20a b x + 15a )\|b \|x +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression Integer +--E 250 + +--S 251 of 518 +--a0046:= integrate(t0046,x) +--E 251 + +--S 252 of 518 +--m0046:= a0046-r0046 +--E 252 + +--S 253 of 518 +--d0046:= D(m0046,x) +--E 253 + +--S 254 of 518 +t0047:= (a+b*x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (160) ---------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 254 + +--S 255 of 518 +r0047:= x^(1/2)*(a+b*x)^(1/2)+a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (161) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 255 + +--S 256 of 518 +--a0047:= integrate(t0047,x) +--E 256 + +--S 257 of 518 +--m0047:= a0047-r0047 +--E 257 + +--S 258 of 518 +--d0047:= D(m0047,x) +--E 258 + +--S 259 of 518 +t0048:= (a+b*x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (162) ------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 259 + +--S 260 of 518 +r0048:= 3/4*a*x^(1/2)*(a+b*x)^(1/2)+1/2*x^(1/2)*(a+b*x)^(3/2)+_ + 3/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x + 5a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (163) ---------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression Integer +--E 260 + +--S 261 of 518 +--a0048:= integrate(t0048,x) +--E 261 + +--S 262 of 518 +--m0048:= a0048-r0048 +--E 262 + +--S 263 of 518 +--d0048:= D(m0048,x) +--E 263 + +--S 264 of 518 +t0049:= (a+b*x)^(5/2)/x^(1/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (164) ------------------------------ +--R +-+ +--R \|x +--R Type: Expression Integer +--E 264 + +--S 265 of 518 +r0049:= 5/8*a^2*x^(1/2)*(a+b*x)^(1/2)+5/12*a*x^(1/2)*(a+b*x)^(3/2)+_ + 1/3*x^(1/2)*(a+b*x)^(5/2)+_ + 5/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 15a atanh(----------) + (8b x + 26a b x + 33a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (165) ------------------------------------------------------------------ +--R +-+ +--R 24\|b +--R Type: Expression Integer +--E 265 + +--S 266 of 518 +--a0049:= integrate(t0049,x) +--E 266 + +--S 267 of 518 +--m0049:= a0049-r0049 +--E 267 + +--S 268 of 518 +--d0049:= D(m0049,x) +--E 268 + +--S 269 of 518 +t0050:= 1/x^(1/2)/(a+b*x)^(1/2) +--R +--R +--R 1 +--R (166) -------------- +--R +-+ +-------+ +--R \|x \|b x + a +--R Type: Expression Integer +--E 269 + +--S 270 of 518 +r0050:= 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atanh(----------) +--R +-------+ +--R \|b x + a +--R (167) ------------------ +--R +-+ +--R \|b +--R Type: Expression Integer +--E 270 + +--S 271 of 518 +--a0050:= integrate(t0050,x) +--E 271 + +--S 272 of 518 +--m0050:= a0050-r0050 +--E 272 + +--S 273 of 518 +--d0050:= D(m0050,x) +--E 273 + +--S 274 of 518 +t0051:= (a+b*x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (168) ---------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 274 + +--S 275 of 518 +r0051:= -2*(a+b*x)^(1/2)/x^(1/2)+2*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x atanh(----------) - 2\|b x + a +--R +-------+ +--R \|b x + a +--R (169) ---------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 275 + +--S 276 of 518 +--a0051:= integrate(t0051,x) +--E 276 + +--S 277 of 518 +--m0051:= a0051-r0051 +--E 277 + +--S 278 of 518 +--d0051:= D(m0051,x) +--E 278 + +--S 279 of 518 +t0052:= (a+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (170) ------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 279 + +--S 280 of 518 +r0052:= 3*b*x^(1/2)*(a+b*x)^(1/2)-2*(a+b*x)^(3/2)/x^(1/2)+_ + 3*a*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 3a\|b \|x atanh(----------) + (b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (171) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 280 + +--S 281 of 518 +--a0052:= integrate(t0052,x) +--E 281 + +--S 282 of 518 +--m0052:= a0052-r0052 +--E 282 + +--S 283 of 518 +--d0052:= D(m0052,x) +--E 283 + +--S 284 of 518 +t0053:= (a+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (172) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 284 + +--S 285 of 518 +r0053:= 15/4*a*b*x^(1/2)*(a+b*x)^(1/2)+5/2*b*x^(1/2)*(a+b*x)^(3/2)-_ + 2*(a+b*x)^(5/2)/x^(1/2)+_ + 15/4*a^2*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a \|b \|x atanh(----------) + (2b x + 9a b x - 8a )\|b x + a +--R +-------+ +--R \|b x + a +--R (173) ---------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression Integer +--E 285 + +--S 286 of 518 +--a0053:= integrate(t0053,x) +--E 286 + +--S 287 of 518 +--m0053:= a0053-r0053 +--E 287 + +--S 288 of 518 +--d0053:= D(m0053,x) +--E 288 + +--S 289 of 518 +t0054:= (a+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (174) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 289 + +--S 290 of 518 +r0054:= -2*b*(a+b*x)^(1/2)/x^(1/2)-2/3*(a+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6b x\|b \|x atanh(----------) + (- 8b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (175) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 290 + +--S 291 of 518 +--a0054:= integrate(t0054,x) +--E 291 + +--S 292 of 518 +--m0054:= a0054-r0054 +--E 292 + +--S 293 of 518 +--d0054:= D(m0054,x) +--E 293 + +--S 294 of 518 +t0055:= (a+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (176) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 294 + +--S 295 of 518 +r0055:= 5*b^2*x^(1/2)*(a+b*x)^(1/2)-10/3*b*(a+b*x)^(3/2)/x^(1/2)-_ + 2/3*(a+b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a b x\|b \|x atanh(----------) + (3b x - 14a b x - 2a )\|b x + a +--R +-------+ +--R \|b x + a +--R (177) -------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 295 + +--S 296 of 518 +--a0055:= integrate(t0055,x) +--E 296 + +--S 297 of 518 +--m0055:= a0055-r0055 +--E 297 + +--S 298 of 518 +--d0055:= D(m0055,x) +--E 298 + +--S 299 of 518 +t0056:= x^(1/2)*(2-b*x)^(1/2) +--R +--R +--R +---------+ +-+ +--R (178) \|- b x + 2 \|x +--R Type: Expression Integer +--E 299 + +--S 300 of 518 +r0056:= -1/2*x^(1/2)*(2-b*x)^(1/2)/b+1/2*x^(3/2)*(2-b*x)^(1/2)+_ + asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) + (b x - 1)\|- b x + 2 \|b \|x +--R 2 +--R (179) --------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression Integer +--E 300 + +--S 301 of 518 +--a0056:= integrate(t0056,x) +--E 301 + +--S 302 of 518 +--m0056:= a0056-r0056 +--E 302 + +--S 303 of 518 +--d0056:= D(m0056,x) +--E 303 + +--S 304 of 518 +t0057:= x^(1/2)/(1-x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (180) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 304 + +--S 305 of 518 +r0057:= -(1-x)^(1/2)*x^(1/2)-asin((1-x)^(1/2)) +--R +--R +--R +-------+ +-------+ +-+ +--R (181) - asin(\|- x + 1 ) - \|- x + 1 \|x +--R Type: Expression Integer +--E 305 + +--S 306 of 518 +--a0057:= integrate(t0057,x) +--E 306 + +--S 307 of 518 +--m0057:= a0057-r0057 +--E 307 + +--S 308 of 518 +--d0057:= D(m0057,x) +--E 308 + +--S 309 of 518 +t0058:= x^(1/2)/(2-b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (182) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression Integer +--E 309 + +--S 310 of 518 +r0058:= -x^(1/2)*(2-b*x)^(1/2)/b+2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) - \|- b x + 2 \|b \|x +--R 2 +--R (183) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression Integer +--E 310 + +--S 311 of 518 +--a0058:= integrate(t0058,x) +--E 311 + +--S 312 of 518 +--m0058:= a0058-r0058 +--E 312 + +--S 313 of 518 +--d0058:= D(m0058,x) +--E 313 + +--S 314 of 518 +t0059:= x^(3/2)/(2-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (184) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression Integer +--E 314 + +--S 315 of 518 +r0059:= 2*x^(3/2)/b/(2-b*x)^(1/2)+3*x^(1/2)*(2-b*x)^(1/2)/b^2-_ + 6*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x +-+ +-+ +--R - 6\|- b x + 2 asin(------------) + (- b x + 6)\|b \|x +--R 2 +--R (185) ------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + 2 \|b +--R Type: Expression Integer +--E 315 + +--S 316 of 518 +--a0059:= integrate(t0059,x) +--E 316 + +--S 317 of 518 +--m0059:= a0059-r0059 +--E 317 + +--S 318 of 518 +--d0059:= D(m0059,x) +--E 318 + +--S 319 of 518 +t0060:= x^(5/2)/(2-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (186) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression Integer +--E 319 + +--S 320 of 518 +r0060:= -1/2/b^(7/2)*(x^(5/2)*b^(5/2)-30*x^(1/2)*b^(1/2)+5*x^(3/2)*b^(3/2)+_ + 30*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))*(2-b*x)^(1/2))/(2-b*x)^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x 2 2 +-+ +-+ +--R - 30\|- b x + 2 asin(------------) + (- b x - 5b x + 30)\|b \|x +--R 2 +--R (187) ----------------------------------------------------------------- +--R 3 +---------+ +-+ +--R 2b \|- b x + 2 \|b +--R Type: Expression Integer +--E 320 + +--S 321 of 518 +--a0060:= integrate(t0060,x) +--E 321 + +--S 322 of 518 +--m0060:= a0060-r0060 +--E 322 + +--S 323 of 518 +--d0060:= D(m0060,x) +--E 323 + +--S 324 of 518 +t0061:= x^(5/2)/(2-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (188) ----------------------------- +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R Type: Expression Integer +--E 324 + +--S 325 of 518 +r0061:= 2/3*x^(5/2)/b/(2-b*x)^(3/2)-10/3*x^(3/2)/b^2/(2-b*x)^(1/2)-_ + 5*x^(1/2)*(2-b*x)^(1/2)/b^3+_ + 10*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(7/2) +--R +--R +--R (189) +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x 2 2 +-+ +-+ +--R (30b x - 60)\|- b x + 2 asin(------------) + (3b x - 40b x + 60)\|b \|x +--R 2 +--R ------------------------------------------------------------------------- +--R 4 3 +---------+ +-+ +--R (3b x - 6b )\|- b x + 2 \|b +--R Type: Expression Integer +--E 325 + +--S 326 of 518 +--a0061:= integrate(t0061,x) +--E 326 + +--S 327 of 518 +--m0061:= a0061-r0061 +--E 327 + +--S 328 of 518 +--d0061:= D(m0061,x) +--E 328 + +--S 329 of 518 +t0062:= (2-b*x)^(1/2)/x^(1/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (190) ------------ +--R +-+ +--R \|x +--R Type: Expression Integer +--E 329 + +--S 330 of 518 +r0062:= x^(1/2)*(2-b*x)^(1/2)+2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) + \|- b x + 2 \|b \|x +--R 2 +--R (191) ------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression Integer +--E 330 + +--S 331 of 518 +--a0062:= integrate(t0062,x) +--E 331 + +--S 332 of 518 +--m0062:= a0062-r0062 +--E 332 + +--S 333 of 518 +--d0062:= D(m0062,x) +--E 333 + +--S 334 of 518 +t0063:= (2-b*x)^(3/2)/x^(1/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (192) ----------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 334 + +--S 335 of 518 +r0063:= 3/2*x^(1/2)*(2-b*x)^(1/2)+1/2*x^(1/2)*(2-b*x)^(3/2)+_ + 3*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 6asin(------------) + (- b x + 5)\|- b x + 2 \|b \|x +--R 2 +--R (193) ----------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 335 + +--S 336 of 518 +--a0063:= integrate(t0063,x) +--E 336 + +--S 337 of 518 +--m0063:= a0063-r0063 +--E 337 + +--S 338 of 518 +--d0063:= D(m0063,x) +--E 338 + +--S 339 of 518 +t0064:= 1/x^(1/2)/(2-b*x)^(1/2) +--R +--R +--R 1 +--R (194) ---------------- +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R Type: Expression Integer +--E 339 + +--S 340 of 518 +r0064:= 2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +--R 2asin(------------) +--R 2 +--R (195) ------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 340 + +--S 341 of 518 +--a0064:= integrate(t0064,x) +--E 341 + +--S 342 of 518 +--m0064:= a0064-r0064 +--E 342 + +--S 343 of 518 +--d0064:= D(m0064,x) +--E 343 + +--S 344 of 518 +t0065:= (2-b*x)^(1/2)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (196) ------------ +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 344 + +--S 345 of 518 +r0065:= -2*(2-b*x)^(1/2)/x^(1/2)-2*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R - 2\|b \|x asin(------------) - 2\|- b x + 2 +--R 2 +--R (197) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 345 + +--S 346 of 518 +--a0065:= integrate(t0065,x) +--E 346 + +--S 347 of 518 +--m0065:= a0065-r0065 +--E 347 + +--S 348 of 518 +--d0065:= D(m0065,x) +--E 348 + +--S 349 of 518 +t0066:= (2-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (198) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 349 + +--S 350 of 518 +r0066:= -3*b*x^(1/2)*(2-b*x)^(1/2)-2*(2-b*x)^(3/2)/x^(1/2)-_ + 6*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R - 6\|b \|x asin(------------) + (- b x - 4)\|- b x + 2 +--R 2 +--R (199) ------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 350 + +--S 351 of 518 +--a0066:= integrate(t0066,x) +--E 351 + +--S 352 of 518 +--m0066:= a0066-r0066 +--E 352 + +--S 353 of 518 +--d0066:= D(m0066,x) +--E 353 + +--S 354 of 518 +t0067:= (2-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (200) ----------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 354 + +--S 355 of 518 +r0067:= -15/2*b*x^(1/2)*(2-b*x)^(1/2)-5/2*b*x^(1/2)*(2-b*x)^(3/2)-_ + 2*(2-b*x)^(5/2)/x^(1/2)-15*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +---------+ +--R - 30\|b \|x asin(------------) + (b x - 9b x - 16)\|- b x + 2 +--R 2 +--R (201) --------------------------------------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 355 + +--S 356 of 518 +--a0067:= integrate(t0067,x) +--E 356 + +--S 357 of 518 +--m0067:= a0067-r0067 +--E 357 + +--S 358 of 518 +--d0067:= D(m0067,x) +--E 358 + +--S 359 of 518 +t0068:= (2-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (202) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 359 + +--S 360 of 518 +r0068:= 2*b*(2-b*x)^(1/2)/x^(1/2)-2/3*(2-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R 6b x\|b \|x asin(------------) + (8b x - 4)\|- b x + 2 +--R 2 +--R (203) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 360 + +--S 361 of 518 +--a0068:= integrate(t0068,x) +--E 361 + +--S 362 of 518 +--m0068:= a0068-r0068 +--E 362 + +--S 363 of 518 +--d0068:= D(m0068,x) +--E 363 + +--S 364 of 518 +t0069:= (2-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (204) ----------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 364 + +--S 365 of 518 +r0069:= 1/3*(3*b^2*x^2*(2-b*x)^(1/2)+28*b*x*(2-b*x)^(1/2)-8*(2-b*x)^(1/2)+_ + 30*b^(3/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))*x^(3/2))/x^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +---------+ +--R 30b x\|b \|x asin(------------) + (3b x + 28b x - 8)\|- b x + 2 +--R 2 +--R (205) ----------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 365 + +--S 366 of 518 +--a0069:= integrate(t0069,x) +--E 366 + +--S 367 of 518 +--m0069:= a0069-r0069 +--E 367 + +--S 368 of 518 +--d0069:= D(m0069,x) +--E 368 + +--S 369 of 518 +t0070:= x^(1/2)*(a-b*x)^(1/2) +--R +--R +--R +---------+ +-+ +--R (206) \|- b x + a \|x +--R Type: Expression Integer +--E 369 + +--S 370 of 518 +r0070:= -1/4*a*x^(1/2)*(a-b*x)^(1/2)/b+1/2*x^(3/2)*(a-b*x)^(1/2)+_ + 1/4*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + (2b x - a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (207) ----------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression Integer +--E 370 + +--S 371 of 518 +--a0070:= integrate(t0070,x) +--E 371 + +--S 372 of 518 +--m0070:= a0070-r0070 +--E 372 + +--S 373 of 518 +--d0070:= D(m0070,x) +--E 373 + +--S 374 of 518 +t0071:= x^(1/2)/(a-b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (208) ------------ +--R +---------+ +--R \|- b x + a +--R Type: Expression Integer +--E 374 + +--S 375 of 518 +r0071:= -x^(1/2)*(a-b*x)^(1/2)/b+a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) - \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (209) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression Integer +--E 375 + +--S 376 of 518 +--a0071:= integrate(t0071,x) +--E 376 + +--S 377 of 518 +--m0071:= a0071-r0071 +--E 377 + +--S 378 of 518 +--d0071:= D(m0071,x) +--E 378 + +--S 379 of 518 +t0072:= x^(1/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (210) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression Integer +--E 379 + +--S 380 of 518 +r0072:= 2*x^(1/2)/b/(a-b*x)^(1/2)-2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 2\|- b x + a atan(------------) + 2\|b \|x +--R +---------+ +--R \|- b x + a +--R (211) --------------------------------------------- +--R +---------+ +-+ +--R b\|- b x + a \|b +--R Type: Expression Integer +--E 380 + +--S 381 of 518 +--a0072:= integrate(t0072,x) +--E 381 + +--S 382 of 518 +--m0072:= a0072-r0072 +--E 382 + +--S 383 of 518 +--d0072:= D(m0072,x) +--E 383 + +--S 384 of 518 +t0073:= x^(3/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (212) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression Integer +--E 384 + +--S 385 of 518 +r0073:= 2*x^(3/2)/b/(a-b*x)^(1/2)+3*x^(1/2)*(a-b*x)^(1/2)/b^2-_ + 3*a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 3a\|- b x + a atan(------------) + (- b x + 3a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (213) --------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + a \|b +--R Type: Expression Integer +--E 385 + +--S 386 of 518 +--a0073:= integrate(t0073,x) +--E 386 + +--S 387 of 518 +--m0073:= a0073-r0073 +--E 387 + +--S 388 of 518 +--d0073:= D(m0073,x) +--E 388 + +--S 389 of 518 +t0074:= x^(3/2)/(a-b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (214) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression Integer +--E 389 + +--S 390 of 518 +r0074:= 2/3*x^(3/2)/b/(a-b*x)^(3/2)-2*x^(1/2)/b^2/(a-b*x)^(1/2)+_ + 2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R (6b x - 6a)\|- b x + a atan(------------) + (- 8b x + 6a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (215) ----------------------------------------------------------------- +--R 3 2 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression Integer +--E 390 + +--S 391 of 518 +--a0074:= integrate(t0074,x) +--E 391 + +--S 392 of 518 +--m0074:= a0074-r0074 +--E 392 + +--S 393 of 518 +--d0074:= D(m0074,x) +--E 393 + +--S 394 of 518 +t0075:= x^(5/2)/(a-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (216) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression Integer +--E 394 + +--S 395 of 518 +r0075:= -1/4/b^(7/2)*(2*x^(5/2)*b^(5/2)-15*a^2*x^(1/2)*b^(1/2)+_ + 5*a*x^(3/2)*b^(3/2)+_ + 15*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))*(a-b*x)^(1/2))/(a-b*x)^(1/2) +--R +--R +--R (217) +--R +-+ +-+ +--R 2 +---------+ \|b \|x 2 2 2 +-+ +-+ +--R - 15a \|- b x + a atan(------------) + (- 2b x - 5a b x + 15a )\|b \|x +--R +---------+ +--R \|- b x + a +--R ------------------------------------------------------------------------ +--R 3 +---------+ +-+ +--R 4b \|- b x + a \|b +--R Type: Expression Integer +--E 395 + +--S 396 of 518 +--a0075:= integrate(t0075,x) +--E 396 + +--S 397 of 518 +--m0075:= a0075-r0075 +--E 397 + +--S 398 of 518 +--d0075:= D(m0075,x) +--E 398 + +--S 399 of 518 +t0076:= x^(5/2)/(a-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (218) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression Integer +--E 399 + +--S 400 of 518 +r0076:= 2/3*x^(5/2)/b/(a-b*x)^(3/2)-10/3*x^(3/2)/b^2/(a-b*x)^(1/2)-_ + 5*x^(1/2)*(a-b*x)^(1/2)/b^3+_ + 5*a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(7/2) +--R +--R +--R (219) +--R +-+ +-+ +--R 2 +---------+ \|b \|x +--R (15a b x - 15a )\|- b x + a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x - 20a b x + 15a )\|b \|x +--R / +--R 4 3 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression Integer +--E 400 + +--S 401 of 518 +--a0076:= integrate(t0076,x) +--E 401 + +--S 402 of 518 +--m0076:= a0076-r0076 +--E 402 + +--S 403 of 518 +--d0076:= D(m0076,x) +--E 403 + +--S 404 of 518 +t0077:= (a-b*x)^(1/2)/x^(1/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (220) ------------ +--R +-+ +--R \|x +--R Type: Expression Integer +--E 404 + +--S 405 of 518 +r0077:= x^(1/2)*(a-b*x)^(1/2)+a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (221) ------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 405 + +--S 406 of 518 +--a0077:= integrate(t0077,x) +--E 406 + +--S 407 of 518 +--m0077:= a0077-r0077 +--E 407 + +--S 408 of 518 +--d0077:= D(m0077,x) +--E 408 + +--S 409 of 518 +t0078:= (a-b*x)^(3/2)/x^(1/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (222) ----------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 409 + +--S 410 of 518 +r0078:= 3/4*a*x^(1/2)*(a-b*x)^(1/2)+1/2*x^(1/2)*(a-b*x)^(3/2)+_ + 3/4*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R 3a atan(------------) + (- 2b x + 5a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (223) --------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression Integer +--E 410 + +--S 411 of 518 +--a0078:= integrate(t0078,x) +--E 411 + +--S 412 of 518 +--m0078:= a0078-r0078 +--E 412 + +--S 413 of 518 +--d0078:= D(m0078,x) +--E 413 + +--S 414 of 518 +t0079:= 1/x^(1/2)/(a-b*x)^(1/2) +--R +--R +--R 1 +--R (224) ---------------- +--R +---------+ +-+ +--R \|- b x + a \|x +--R Type: Expression Integer +--E 414 + +--S 415 of 518 +r0079:= 2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atan(------------) +--R +---------+ +--R \|- b x + a +--R (225) ------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 415 + +--S 416 of 518 +--a0079:= integrate(t0079,x) +--E 416 + +--S 417 of 518 +--m0079:= a0079-r0079 +--E 417 + +--S 418 of 518 +--d0079:= D(m0079,x) +--E 418 + +--S 419 of 518 +t0080:= (a-b*x)^(1/2)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (226) ------------ +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 419 + +--S 420 of 518 +r0080:= -2*(a-b*x)^(1/2)/x^(1/2)-2*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x atan(------------) - 2\|- b x + a +--R +---------+ +--R \|- b x + a +--R (227) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 420 + +--S 421 of 518 +--a0080:= integrate(t0080,x) +--E 421 + +--S 422 of 518 +--m0080:= a0080-r0080 +--E 422 + +--S 423 of 518 +--d0080:= D(m0080,x) +--E 423 + +--S 424 of 518 +t0081:= (a-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (228) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 424 + +--S 425 of 518 +r0081:= -3*b*x^(1/2)*(a-b*x)^(1/2)-2*(a-b*x)^(3/2)/x^(1/2)-_ + 3*a*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 3a\|b \|x atan(------------) + (- b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (229) --------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 425 + +--S 426 of 518 +--a0081:= integrate(t0081,x) +--E 426 + +--S 427 of 518 +--m0081:= a0081-r0081 +--E 427 + +--S 428 of 518 +--d0081:= D(m0081,x) +--E 428 + +--S 429 of 518 +t0082:= (a-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (230) -------------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 429 + +--S 430 of 518 +r0082:= -15/4*a*b*x^(1/2)*(a-b*x)^(1/2)-5/2*b*x^(1/2)*(a-b*x)^(3/2)-_ + 2*(a-b*x)^(5/2)/x^(1/2)-_ + 15/4*a^2*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R (231) +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +---------+ +--R - 15a \|b \|x atan(------------) + (2b x - 9a b x - 8a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R --------------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression Integer +--E 430 + +--S 431 of 518 +--a0082:= integrate(t0082,x) +--E 431 + +--S 432 of 518 +--m0082:= a0082-r0082 +--E 432 + +--S 433 of 518 +--d0082:= D(m0082,x) +--E 433 + +--S 434 of 518 +t0083:= (a-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (232) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 434 + +--S 435 of 518 +r0083:= 2*b*(a-b*x)^(1/2)/x^(1/2)-2/3*(a-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R 6b x\|b \|x atan(------------) + (8b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (233) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 435 + +--S 436 of 518 +--a0083:= integrate(t0083,x) +--E 436 + +--S 437 of 518 +--m0083:= a0083-r0083 +--E 437 + +--S 438 of 518 +--d0083:= D(m0083,x) +--E 438 + +--S 439 of 518 +t0084:= (a-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (234) -------------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression Integer +--E 439 + +--S 440 of 518 +r0084:= 5*b^2*x^(1/2)*(a-b*x)^(1/2)+10/3*b*(a-b*x)^(3/2)/x^(1/2)-_ + 2/3*(a-b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R (235) +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +---------+ +--R 15a b x\|b \|x atan(------------) + (3b x + 14a b x - 2a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R ----------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression Integer +--E 440 + +--S 441 of 518 +--a0084:= integrate(t0084,x) +--E 441 + +--S 442 of 518 +--m0084:= a0084-r0084 +--E 442 + +--S 443 of 518 +--d0084:= D(m0084,x) +--E 443 + +--S 444 of 518 +t0085:= x^3/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 3 +--R x +--R (236) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 444 + +--S 445 of 518 +r0085:= -2/3*a*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 5/8*(b*c+a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 5/12*(b*c+a*d)*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/3*x^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d+_ + 3/2*a*c*(b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(5/2)/d^(5/2)-5/8*(b*c+a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(7/2) +--R +--R +--R (237) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 15a d - 9a b c d - 9a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (8b d x + (- 10a b d - 10b c d)x + 15a d + 14a b c d + 15b c )\|b +--R * +--R +-+ +-------+ +-------+ +--R \|d \|b x + a \|d x + c +--R / +--R 3 3 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression Integer +--E 445 + +--S 446 of 518 +--a0085:= integrate(t0085,x) +--E 446 + +--S 447 of 518 +--m0085:= a0085-r0085 +--E 447 + +--S 448 of 518 +--d0085:= D(m0085,x) +--E 448 + +--S 449 of 518 +t0086:= x^2/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 2 +--R x +--R (238) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 449 + +--S 450 of 518 +r0086:= -3/4*(b*c+a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/2*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d-_ + a*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/_ + d^(3/2)+3/4*(b*c+a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (239) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (3a d + 2a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x - 3a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 2 +-+ +-+ +--R 4b d \|b \|d +--R Type: Expression Integer +--E 450 + +--S 451 of 518 +--a0086:= integrate(t0086,x) +--E 451 + +--S 452 of 518 +--m0086:= a0086-r0086 +--E 452 + +--S 453 of 518 +--d0086:= D(m0086,x) +--E 453 + +--S 454 of 518 +t0087:= x/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R x +--R (240) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 454 + +--S 455 of 518 +r0087:= (a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d-_ + (b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (- a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (241) ----------------------------------------------------------------- +--R +-+ +-+ +--R b d\|b \|d +--R Type: Expression Integer +--E 455 + +--S 456 of 518 +--a0087:= integrate(t0087,x) +--E 456 + +--S 457 of 518 +--m0087:= a0087-r0087 +--E 457 + +--S 458 of 518 +--d0087:= D(m0087,x) +--E 458 + +--S 459 of 518 +t0088:= 1/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (242) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 459 + +--S 460 of 518 +r0088:= 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (243) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 460 + +--S 461 of 518 +--a0088:= integrate(t0088,x) +--E 461 + +--S 462 of 518 +--m0088:= a0088-r0088 +--E 462 + +--S 463 of 518 +--d0088:= D(m0088,x) +--E 463 + +--S 464 of 518 +t0089:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (244) --------------------- +--R +-------+ +-------+ +--R x\|b x + a \|d x + c +--R Type: Expression Integer +--E 464 + +--S 465 of 518 +r0089:= -2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(1/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R (245) - ---------------------- +--R +-+ +-+ +--R \|a \|c +--R Type: Expression Integer +--E 465 + +--S 466 of 518 +--a0089:= integrate(t0089,x) +--E 466 + +--S 467 of 518 +--m0089:= a0089-r0089 +--E 467 + +--S 468 of 518 +--d0089:= D(m0089,x) +--E 468 + +--S 469 of 518 +t0090:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (246) ---------------------- +--R 2 +-------+ +-------+ +--R x \|b x + a \|d x + c +--R Type: Expression Integer +--E 469 + +--S 470 of 518 +r0090:= -(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c/x+_ + (b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(3/2)/c^(3/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d + b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R (247) ----------------------------------------------------------------- +--R +-+ +-+ +--R a c x\|a \|c +--R Type: Expression Integer +--E 470 + +--S 471 of 518 +--a0090:= integrate(t0090,x) +--E 471 + +--S 472 of 518 +--m0090:= a0090-r0090 +--E 472 + +--S 473 of 518 +--d0090:= D(m0090,x) +--E 473 + +--S 474 of 518 +t0091:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (248) ---------------------- +--R 3 +-------+ +-------+ +--R x \|b x + a \|d x + c +--R Type: Expression Integer +--E 474 + +--S 475 of 518 +r0091:= -1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c/x^2+_ + 3/4*(b*c+a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a^2/c^2/x+_ + b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(3/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(5/2) +--R +--R +--R (249) +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 3a d - 2a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((3a d + 3b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 2 +-+ +-+ +--R 4a c x \|a \|c +--R Type: Expression Integer +--E 475 + +--S 476 of 518 +--a0091:= integrate(t0091,x) +--E 476 + +--S 477 of 518 +--m0091:= a0091-r0091 +--E 477 + +--S 478 of 518 +--d0091:= D(m0091,x) +--E 478 + +--S 479 of 518 +t0092:= x^3/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 3 +--R x +--R (250) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression Integer +--E 479 + +--S 480 of 518 +r0092:= -2*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + 7/4*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^3-_ + 3/4*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/2*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2+_ + 3*c^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/_ + d^(7/2)+3/4*(b*c+a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2) +--R +--R +--R (251) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-------+ \|d \|b x + a +--R (3a d + 3a b c d + 9a b c d - 15b c )\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 2 2 2 3 2 2 2 2 2 +--R (2a b d - 2b c d )x + (- 3a d - 2a b c d + 5b c d)x - 3a c d +--R + +--R 2 2 3 +--R - 4a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 4 3 3 +-+ +-+ +-------+ +--R (4a b d - 4b c d )\|b \|d \|d x + c +--R Type: Expression Integer +--E 480 + +--S 481 of 518 +--a0092:= integrate(t0092,x) +--E 481 + +--S 482 of 518 +--m0092:= a0092-r0092 +--E 482 + +--S 483 of 518 +--d0092:= D(m0092,x) +--E 483 + +--S 484 of 518 +t0093:= x^2/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 2 +--R x +--R (252) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression Integer +--E 484 + +--S 485 of 518 +r0093:= 2*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(1/2)+_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2-_ + 3*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/_ + d^(5/2)-a*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2) +--R +--R +--R (253) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ \|d \|b x + a +--R (- a d - 2a b c d + 3b c )\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 +-+ +-+ +-------+ +--R ((a d - b c d)x + a c d - 3b c )\|b \|d \|b x + a +--R / +--R 3 2 2 +-+ +-+ +-------+ +--R (a b d - b c d )\|b \|d \|d x + c +--R Type: Expression Integer +--E 485 + +--S 486 of 518 +--a0093:= integrate(t0093,x) +--E 486 + +--S 487 of 518 +--m0093:= a0093-r0093 +--E 487 + +--S 488 of 518 +--d0093:= D(m0093,x) +--E 488 + +--S 489 of 518 +t0094:= x/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R x +--R (254) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression Integer +--E 489 + +--S 490 of 518 +r0094:= -2*c*(a+b*x)^(1/2)/d/(b*c-a*d)/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +-+ +-+ +-------+ +--R (2a d - 2b c)\|d x + c atanh(--------------) + 2c\|b \|d \|b x + a +--R +-+ +-------+ +--R \|b \|d x + c +--R (255) ------------------------------------------------------------------- +--R 2 +-+ +-+ +-------+ +--R (a d - b c d)\|b \|d \|d x + c +--R Type: Expression Integer +--E 490 + +--S 491 of 518 +--a0094:= integrate(t0094,x) +--E 491 + +--S 492 of 518 +--m0094:= a0094-r0094 +--E 492 + +--S 493 of 518 +--d0094:= D(m0094,x) +--E 493 + +--S 494 of 518 +t0095:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (256) -------------------------------- +--R 2 +-------+ +-------+ +--R (d x + c x)\|b x + a \|d x + c +--R Type: Expression Integer +--E 494 + +--S 495 of 518 +r0095:= -2*d*(a+b*x)^(1/2)/c/(b*c-a*d)/(c+d*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(3/2) +--R +--R +--R (257) +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +-+ +-+ +-------+ +--R (- 2a d + 2b c)\|d x + c atanh(--------------) + 2d\|a \|c \|b x + a +--R +-+ +-------+ +--R \|a \|d x + c +--R --------------------------------------------------------------------- +--R 2 +-+ +-+ +-------+ +--R (a c d - b c )\|a \|c \|d x + c +--R Type: Expression Integer +--E 495 + +--S 496 of 518 +--a0095:= integrate(t0095,x) +--E 496 + +--S 497 of 518 +--m0095:= a0095-r0095 +--E 497 + +--S 498 of 518 +--d0095:= D(m0095,x) +--E 498 + +--S 499 of 518 +t0096:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (258) --------------------------------- +--R 3 2 +-------+ +-------+ +--R (d x + c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 499 + +--S 500 of 518 +r0096:= 2*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(1/2)-_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^2/x+_ + b*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(3/2)+_ + 3*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(5/2) +--R +--R +--R (259) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ \|c \|b x + a +--R (3a d - 2a b c d - b c )x\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 +-+ +-+ +-------+ +--R ((- 3a d + b c d)x - a c d + b c )\|a \|c \|b x + a +--R / +--R 2 2 3 +-+ +-+ +-------+ +--R (a c d - a b c )x\|a \|c \|d x + c +--R Type: Expression Integer +--E 500 + +--S 501 of 518 +--a0096:= integrate(t0096,x) +--E 501 + +--S 502 of 518 +--m0096:= a0096-r0096 +--E 502 + +--S 503 of 518 +--d0096:= D(m0096,x) +--E 503 + +--S 504 of 518 +t0097:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (260) --------------------------------- +--R 4 3 +-------+ +-------+ +--R (d x + c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 504 + +--S 505 of 518 +r0097:= -2*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + 1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^2/x^2+_ + 3/4*b*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a^2/c^2/x+_ + 7/4*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x-_ + 3*d^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/_ + c^(7/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(7/2) +--R +--R +--R (261) +--R 3 3 2 2 2 2 3 3 2 +-------+ +--R (- 15a d + 9a b c d + 3a b c d + 3b c )x \|d x + c +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 3 2 2 2 2 2 2 2 2 3 +--R (15a d - 4a b c d - 3b c d)x + (5a c d - 2a b c d - 3b c )x +--R + +--R 2 2 3 +--R - 2a c d + 2a b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 3 3 2 4 2 +-+ +-+ +-------+ +--R (4a c d - 4a b c )x \|a \|c \|d x + c +--R Type: Expression Integer +--E 505 + +--S 506 of 518 +--a0097:= integrate(t0097,x) +--E 506 + +--S 507 of 518 +--m0097:= a0097-r0097 +--E 507 + +--S 508 of 518 +--d0097:= D(m0097,x) +--E 508 + +--S 509 of 518 +t0098:= x^5/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 5 +--R x +--R (262) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 509 + +--S 510 of 518 +r0098:= -2/3*a^5*(a+b*x)^(1/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)+_ + 20/3*a^3*(a+b*x)^(3/2)/b^5/d/(c+d*x)^(3/2)+_ + 10/3*a^4*(a+b*x)^(3/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)-_ + 20/3*a^2*(a+b*x)^(5/2)/b^5/d/(c+d*x)^(3/2)+_ + 10/3*a*(a+b*x)^(7/2)/b^5/d/(c+d*x)^(3/2)-_ + 2/3*(a+b*x)^(9/2)/b^5/d/(c+d*x)^(3/2)+_ + 20*a^3*(a+b*x)^(1/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 4/3*a^5*(a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 100/3*a^2*(a+b*x)^(3/2)/b^4/d^2/(c+d*x)^(1/2)+_ + 70/3*a*(a+b*x)^(5/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 6*(a+b*x)^(7/2)/b^4/d^2/(c+d*x)^(1/2)+_ + 50*a^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3+_ + 175/4*a*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4+_ + 105/8*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^5-_ + 175/6*a*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 35/4*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^3/d^4+_ + 7*(a+b*x)^(5/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 20*a^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/_ + d^(5/2)-50*a^2*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(7/2)-_ + 175/4*a*(b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(9/2)-_ + 105/8*(b*c-a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(11/2) +--R +--R +--R (263) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R - 15a d - 15a b c d - 30a b c d - 150a b c d + 525a b c d +--R + +--R 5 5 +--R - 315b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 15a c d - 15a b c d - 30a b c d - 150a b c d + 525a b c d +--R + +--R 5 6 +--R - 315b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (8a b d - 16a b c d + 8b c d )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (- 10a b d + 2a b c d + 26a b c d - 18b c d )x +--R + +--R 4 6 2 2 2 4 3 3 3 4 4 2 2 +--R (15a d + 18a b c d - 96a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a c d + 30a b c d + 62a b c d - 574a b c d + 420b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a c d + 20a b c d + 38a b c d - 420a b c d + 315b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 3 8 4 7 5 2 6 2 3 7 4 2 6 +--R (24a b d - 48a b c d + 24b c d )x + 24a b c d - 48a b c d +--R + +--R 5 3 5 +--R 24b c d +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R Type: Expression Integer +--E 510 + +--S 511 of 518 +--a0098:= integrate(t0098,x) +--E 511 + +--S 512 of 518 +--m0098:= a0098-r0098 +--E 512 + +--S 513 of 518 +--d0098:= D(m0098,x) +--E 513 + +--S 514 of 518 +t0099:= x^4/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 4 +--R x +--R (264) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 514 + +--S 515 of 518 +r0099:= 2/3*a^4*(a+b*x)^(1/2)/b^4/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4*a^2*(a+b*x)^(3/2)/b^4/d/(c+d*x)^(3/2)-8/3*a^3*(a+b*x)^(3/2)/_ + b^4/(b*c-a*d)/(c+d*x)^(3/2)+8/3*a*(a+b*x)^(5/2)/b^4/d/(c+d*x)^(3/2)-_ + 2/3*(a+b*x)^(7/2)/b^4/d/(c+d*x)^(3/2)-_ + 12*a^2*(a+b*x)^(1/2)/b^3/d^2/(c+d*x)^(1/2)+4/3*a^4*(a+b*x)^(1/2)/_ + b^3/(b*c-a*d)^2/(c+d*x)^(1/2)+40/3*a*(a+b*x)^(3/2)/b^3/d^2/_ + (c+d*x)^(1/2)-14/3*(a+b*x)^(5/2)/b^3/d^2/(c+d*x)^(1/2)-_ + 20*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^3-35/4*(b*c-a*d)*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^4+_ + 35/6*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^2/d^3+_ + 12*a^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/_ + d^(5/2)+20*a*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2)+35/4*(b*c-a*d)^2*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(9/2) +--R +--R +--R (265) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (9a d + 12a b c d + 54a b c d - 180a b c d + 105b c d)x + 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 54a b c d - 180a b c d + 105b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 5 2 4 3 2 3 3 +--R (6a b d - 12a b c d + 6b c d )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 9a d - 3a b c d + 33a b c d - 21b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (- 18a c d - 24a b c d + 198a b c d - 140b c d)x - 9a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 15a b c d + 145a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 2 7 3 6 4 2 5 2 2 6 3 2 5 +--R (12a b d - 24a b c d + 12b c d )x + 12a b c d - 24a b c d +--R + +--R 4 3 4 +--R 12b c d +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R Type: Expression Integer +--E 515 + +--S 516 of 518 +--a0099:= integrate(t0099,x) +--E 516 + +--S 517 of 518 +--m0099:= a0099-r0099 +--E 517 + +--S 518 of 518 +--d0099:= D(m0099,x) +--E 518 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}