diff --git a/changelog b/changelog index c812b3b..b06a725 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100608 tpd src/axiom-website/patches.html 20100608.01.tpd.patch +20100608 tpd src/input/Makefile rule-based exponential integration +20100608 tpd src/input/richexponential.input rule-based exponential int. 20100607 tpd src/axiom-website/patches.html 20100607.01.tpd.patch 20100607 tpd src/input/Makefile rule-based algebraic integration 20100607 tpd src/input/richalgebraic400-461.input rule-based algebraic int. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index c00fc81..cd60464 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2858,6 +2858,8 @@ src/input/richalgebraic200-299.input rule-based algebraic integration.
src/input/richalgebraic300-399.input rule-based algebraic integration.
20100607.01.tpd.patch src/input/richalgebraic400-461.input rule-based algebraic integration.
+20100608.01.tpd.patch +src/input/richexponential.input rule-based exponential integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 2b8634c..413abe5 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -374,6 +374,7 @@ REGRES= ackermann.regress \ richalgebraic200-299.regress \ richalgebraic300-399.regress \ richalgebraic400-461.regress \ + richexponential.regress \ richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -691,6 +692,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richalgebraic200-299.input \ ${OUT}/richalgebraic300-399.input \ ${OUT}/richalgebraic400-461.input \ + ${OUT}/richexponential.input \ ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ @@ -1038,6 +1040,7 @@ DOCFILES= \ ${DOC}/richalgebraic200-299.input.dvi \ ${DOC}/richalgebraic300-399.input.dvi \ ${DOC}/richalgebraic400-461.input.dvi \ + ${DOC}/richexponential.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ diff --git a/src/input/richexponential.input.pamphlet b/src/input/richexponential.input.pamphlet new file mode 100644 index 0000000..abe2a32 --- /dev/null +++ b/src/input/richexponential.input.pamphlet @@ -0,0 +1,8678 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richexponential.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richexponential.output +)spool richexponential.output +)set message auto off +)clear all + +--S 1 of 578 +t0000:= exp(1)^(a+b*x)/x +--R +--R +--R b x + a +--R %e +--R (1) --------- +--R x +--R Type: Expression Integer +--E 1 + +--S 2 of 578 +r0000:= exp(a)*Ei(b*x) +--R +--R +--R a +--R (2) Ei(b x)%e +--R Type: Expression Integer +--E 2 + +--S 3 of 578 +a0000:= integrate(t0000,x) +--R +--R +--R x %A b + a +--R ++ %e +--R (3) | ---------- d%A +--R ++ %A +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 578 +m0000:= a0000-r0000 +--R +--R +--R x %A b + a +--R ++ %e a +--R (4) | ---------- d%A - Ei(b x)%e +--R ++ %A +--R Type: Expression Integer +--E 4 + +--S 5 of 578 +d0000:= D(m0000,x) +--R +--R +--R b x + a a b x +--R %e - %e %e +--R (5) -------------------- +--R x +--R Type: Expression Integer +--E 5 + +--S 6 of 578 +t0001:= x^3*exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R 3 b x + 3a b x + 3a b x + a +--R (6) x %e +--R Type: Expression Integer +--E 6 + +--S 7 of 578 +r0001:= -2/3*a*exp((a+b*x)^3)/b^4+1/3*exp((a+b*x)^3)*x/b^3+_ + 1/9*(1+3*a^3)*(a+b*x)*Gamma(1/3,-(a+b*x)^3)/b^4/(-(a+b*x)^3)^(1/3)_ + -a^2*(a+b*x)^2*Gamma(2/3,-(a+b*x)^3)/b^4/(-(a+b*x)^3)^(2/3) +--R +--R +--R (7) +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (3b x - 6a)%e +--R * +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 3 4 _ 1 3 3 2 2 2 3 +--R ((3a + 1)b x + 3a + a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 4 _ 2 3 3 2 2 2 3 +--R (- 9a b x - 18a b x - 9a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 4 3| 3 3 2 2 2 3 +--R 9b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 7 + +--S 8 of 578 +a0001:= integrate(t0001,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ 3 %A b + 3%A a b + 3%A a b + a +--R (8) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 578 +m0001:= a0001-r0001 +--R +--R +--R (9) +--R +------------------------------+2 +--R 4 3| 3 3 2 2 2 3 +--R 9b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ 3 %A b + 3%A a b + 3%A a b + a +--R | %A %e d%A +--R ++ +--R + +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (- 3b x + 6a)%e +--R * +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 3 4 _ 1 3 3 2 2 2 3 +--R ((- 3a - 1)b x - 3a - a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 4 _ 2 3 3 2 2 2 3 +--R (9a b x + 18a b x + 9a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 4 3| 3 3 2 2 2 3 +--R 9b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 9 + +--S 10 of 578 +d0001:= D(m0001,x) +--R +--R +--R (10) 0 +--R Type: Expression Integer +--E 10 + +--S 11 of 578 +t0002:= x^2*exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R 2 b x + 3a b x + 3a b x + a +--R (11) x %e +--R Type: Expression Integer +--E 11 + +--S 12 of 578 +r0002:= 1/3*exp((a+b*x)^3)/b^3-1/3*a^2*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b^3/(-(a+b*x)^3)^(1/3)+2/3*a*(a+b*x)^2*_ + Gamma(2/3,-(a+b*x)^3)/b^3/(-(a+b*x)^3)^(2/3) +--R +--R +--R (12) +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R %e \|- b x - 3a b x - 3a b x - a +--R + +--R 2 3 _ 1 3 3 2 2 2 3 +--R (- a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (2a b x + 4a b x + 2a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 12 + +--S 13 of 578 +a0002:= integrate(t0002,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ 2 %A b + 3%A a b + 3%A a b + a +--R (13) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 578 +m0002:= a0002-r0002 +--R +--R +--R (14) +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ 2 %A b + 3%A a b + 3%A a b + a +--R | %A %e d%A +--R ++ +--R + +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R - %e \|- b x - 3a b x - 3a b x - a +--R + +--R 2 3 _ 1 3 3 2 2 2 3 +--R (a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (- 2a b x - 4a b x - 2a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 14 + +--S 15 of 578 +d0002:= D(m0002,x) +--R +--R +--R (15) 0 +--R Type: Expression Integer +--E 15 + +--S 16 of 578 +t0003:= x*exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (16) x %e +--R Type: Expression Integer +--E 16 + +--S 17 of 578 +r0003:= 1/3*a*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b^2/(-(a+b*x)^3)^(1/3)-1/3*(a+b*x)^2*_ + Gamma(2/3,-(a+b*x)^3)/b^2/(-(a+b*x)^3)^(2/3) +--R +--R +--R (17) +--R 2 _ 1 3 3 2 2 2 3 +--R (a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (- b x - 2a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 17 + +--S 18 of 578 +a0003:= integrate(t0003,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R (18) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 578 +m0003:= a0003-r0003 +--R +--R +--R (19) +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R | %A %e d%A +--R ++ +--R + +--R 2 _ 1 3 3 2 2 2 3 +--R (- a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 19 + +--S 20 of 578 +d0003:= D(m0003,x) +--R +--R +--R (20) 0 +--R Type: Expression Integer +--E 20 + +--S 21 of 578 +t0004:= exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (21) %e +--R Type: Expression Integer +--E 21 + +--S 22 of 578 +r0004:= -1/3*(a+b*x)*Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3) +--R +--R +--R _ 1 3 3 2 2 2 3 +--R (- b x - a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R (22) ----------------------------------------------- +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3b\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 22 + +--S 23 of 578 +a0004:= integrate(t0004,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R (23) | %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 578 +m0004:= a0004-r0004 +--R +--R +--R (24) +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3b\|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R | %e d%A +--R ++ +--R + +--R _ 1 3 3 2 2 2 3 +--R (b x + a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3b\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 24 + +--S 25 of 578 +d0004:= D(m0004,x) +--R +--R +--R (25) 0 +--R Type: Expression Integer +--E 25 + +--S 26 of 578 +t0005:= exp(1)^(a+b*x)/(a+b*x) +--R +--R +--R b x + a +--R %e +--R (26) --------- +--R b x + a +--R Type: Expression Integer +--E 26 + +--S 27 of 578 +r0005:= Ei(a+b*x)/b +--R +--R +--R Ei(b x + a) +--R (27) ----------- +--R b +--R Type: Expression Integer +--E 27 + +--S 28 of 578 +a0005:= integrate(t0005,x) +--R +--R +--R Ei(b x + a) +--R (28) ----------- +--R b +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 578 +m0005:= a0005-r0005 +--R +--R +--R (29) 0 +--R Type: Expression Integer +--E 29 + +--S 30 of 578 +d0005:= D(m0005,x) +--R +--R +--R (30) 0 +--R Type: Expression Integer +--E 30 + +--S 31 of 578 +t0006:= exp((a+b*x)^3)*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R 3 3 2 2 2 3 b x + 3a b x + 3a b x + a +--R (31) (b x + 3a b x + 3a b x + a )%e +--R Type: Expression Integer +--E 31 + +--S 32 of 578 +r0006:= 1/3*exp((a+b*x)^3)*(a+b*x)/b+1/9*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3) +--R +--R +--R (32) +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (3b x + 3a)%e +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R _ 1 3 3 2 2 2 3 +--R (b x + a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 9b\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 32 + +--S 33 of 578 +a0006:= integrate(t0006,x) +--R +--R +--R (33) +--R x 3 3 2 2 2 3 +--R ++ 3 3 2 2 2 3 %A b + 3%A a b + 3%A a b + a +--R | (%A b + 3%A a b + 3%A a b + a )%e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 578 +m0006:= a0006-r0006 +--R +--R +--R (34) +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 9b\|- b x - 3a b x - 3a b x - a +--R * +--R INTSIGN +--R , +--R x +--R , +--R 3 3 2 2 2 3 +--R 3 3 2 2 2 3 %A b + 3%A a b + 3%A a b + a +--R (%A b + 3%A a b + 3%A a b + a )%e +--R * +--R d%A +--R + +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (- 3b x - 3a)%e +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R _ 1 3 3 2 2 2 3 +--R (- b x - a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 9b\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 34 + +--S 35 of 578 +d0006:= D(m0006,x) +--R +--R +--R (35) 0 +--R Type: Expression Integer +--E 35 + +--S 36 of 578 +t0007:= exp((a+b*x)^3)*(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (36) (b x + a)%e +--R Type: Expression Integer +--E 36 + +--S 37 of 578 +r0007:= -1/3*(a+b*x)^2*Gamma(2/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(2/3) +--R +--R +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (- b x - 2a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R (37) ---------------------------------------------------------- +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 37 + +--S 38 of 578 +a0007:= integrate(t0007,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R (38) | (%A b + a)%e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 578 +m0007:= a0007-r0007 +--R +--R +--R (39) +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R | (%A b + a)%e d%A +--R ++ +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 39 + +--S 40 of 578 +d0007:= D(m0007,x) +--R +--R +--R (40) 0 +--R Type: Expression Integer +--E 40 + +--S 41 of 578 +t0008:= exp((a+b*x)^3)/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R %e +--R (41) ------------------------------ +--R b x + a +--R Type: Expression Integer +--E 41 + +--S 42 of 578 +r0008:= 1/3*Ei((a+b*x)^3)/b +--R +--R +--R 3 3 2 2 2 3 +--R Ei(b x + 3a b x + 3a b x + a ) +--R (42) -------------------------------- +--R 3b +--R Type: Expression Integer +--E 42 + +--S 43 of 578 +a0008:= integrate(t0008,x) +--R +--R +--R 3 3 2 2 2 3 +--R Ei(b x + 3a b x + 3a b x + a ) +--R (43) -------------------------------- +--R 3b +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 578 +m0008:= a0008-r0008 +--R +--R +--R (44) 0 +--R Type: Expression Integer +--E 44 + +--S 45 of 578 +d0008:= D(m0008,x) +--R +--R +--R (45) 0 +--R Type: Expression Integer +--E 45 + +--S 46 of 578 +t0009:= exp((a+b*x)^3)/(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R %e +--R (46) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression Integer +--E 46 + +--S 47 of 578 +r0009:= -exp((a+b*x)^3)/b/(a+b*x)-(a+b*x)^2*_ + Gamma(2/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(2/3) +--R +--R +--R (47) +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R - %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (- b x - 3a b x - 3a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R (b x + a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 47 + +--S 48 of 578 +a0009:= integrate(t0009,x) +--R +--R +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R (48) | --------------------------------- d%A +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 578 +m0009:= a0009-r0009 +--R +--R +--R (49) +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R (b x + a b)\|- b x - 3a b x - 3a b x - a +--R * +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R | --------------------------------- d%A +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R + +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (b x + 3a b x + 3a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R (b x + a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 49 + +--S 50 of 578 +d0009:= D(m0009,x) +--R +--R +--R (50) 0 +--R Type: Expression Integer +--E 50 + +--S 51 of 578 +t0010:= exp((a+b*x)^3)/(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R %e +--R (51) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression Integer +--E 51 + +--S 52 of 578 +r0010:= -1/2*exp((a+b*x)^3)/b/(a+b*x)^2-1/2*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3) +--R +--R +--R (52) +--R 3 3 2 2 2 3 +------------------------------+ +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R - %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 1 3 3 2 2 2 3 +--R (- b x - 3a b x - 3a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3 2 2 2 3| 3 3 2 2 2 3 +--R (2b x + 4a b x + 2a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 52 + +--S 53 of 578 +a0010:= integrate(t0010,x) +--R +--R +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R (53) | --------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 578 +m0010:= a0010-r0010 +--R +--R +--R (54) +--R +------------------------------+ +--R 3 2 2 2 3| 3 3 2 2 2 3 +--R (2b x + 4a b x + 2a b)\|- b x - 3a b x - 3a b x - a +--R * +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R | --------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R + +--R 3 3 2 2 2 3 +------------------------------+ +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 1 3 3 2 2 2 3 +--R (b x + 3a b x + 3a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3 2 2 2 3| 3 3 2 2 2 3 +--R (2b x + 4a b x + 2a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression Integer +--E 54 + +--S 55 of 578 +d0010:= D(m0010,x) +--R +--R +--R (55) 0 +--R Type: Expression Integer +--E 55 + +--S 56 of 578 +t0011:= x^m*exp(1)^(x^n) +--R +--R +--R n +--R m x +--R (56) x %e +--R Type: Expression Integer +--E 56 + +--S 57 of 578 +r0011:= -x^(1+m)*Gamma((1+m)/n,-x^n)*(-x^n)^(-(1+m)/n)/n +--R +--R +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R x (- x ) | (-----,- x ) +--R n +--R (57) - --------------------------------- +--R n +--R Type: Expression Integer +--E 57 + +--S 58 of 578 +a0011:= integrate(t0011,x) +--R +--R +--R x n +--R ++ m %A +--R (58) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 578 +m0011:= a0011-r0011 +--R +--R +--R - m - 1 +--R x n ------- +--R ++ m %A m + 1 n n _ m + 1 n +--R n | %A %e d%A + x (- x ) | (-----,- x ) +--R ++ n +--R (59) ------------------------------------------------------ +--R n +--R Type: Expression Integer +--E 59 + +--S 60 of 578 +d0011:= D(m0011,x) +--R +--R +--R (60) +--R - m - 1 - n - m - 1 +--R ------- ----------- +--R m n n m + 1 n - 1 n n +--R ((m + 1)x (- x ) + (m + 1)x x (- x ) ) +--R * +--R _ m + 1 n +--R | (-----,- x ) +--R n +--R + +--R - n + m + 1 - m - 1 +--R n ----------- ------- n +--R m + 1 n - 1 x n n n n m x +--R n x x %e (- x ) (- x ) + n x %e +--R / +--R n +--R Type: Expression Integer +--E 60 + +--S 61 of 578 +t0012:= x^m*f^(x^n) +--R +--R +--R n +--R m x +--R (61) x f +--R Type: Expression Integer +--E 61 + +--S 62 of 578 +r0012:= -x^(1+m)*Gamma((1+m)/n,-x^n*log(f))*(-x^n*log(f))^(-(1+m)/n)/n +--R +--R +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R x (- log(f)x ) | (-----,- log(f)x ) +--R n +--R (62) - --------------------------------------------- +--R n +--R Type: Expression Integer +--E 62 + +--S 63 of 578 +a0012:= integrate(t0012,x) +--R +--R +--R x n +--R ++ m %A +--R (63) | %A f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 578 +m0012:= a0012-r0012 +--R +--R +--R - m - 1 +--R x n ------- +--R ++ m %A m + 1 n n _ m + 1 n +--R n | %A f d%A + x (- log(f)x ) | (-----,- log(f)x ) +--R ++ n +--R (64) ----------------------------------------------------------------- +--R n +--R Type: Expression Integer +--E 64 + +--S 65 of 578 +d0012:= D(m0012,x) +--R +--R +--R (65) +--R - m - 1 +--R ------- +--R m n n +--R (m + 1)x (- log(f)x ) +--R + +--R - n - m - 1 +--R ----------- +--R m + 1 n - 1 n n +--R (m + 1)log(f)x x (- log(f)x ) +--R * +--R _ m + 1 n +--R | (-----,- log(f)x ) +--R n +--R + +--R n +--R m x +--R n x f +--R + +--R - n + m + 1 - m - 1 +--R n ----------- ------- +--R m + 1 n - 1 log(f)x n n n n +--R n log(f)x x %e (- log(f)x ) (- log(f)x ) +--R / +--R n +--R Type: Expression Integer +--E 65 + +--S 66 of 578 +t0013:= (a+b*x)^m*exp(1)^((a+b*x)^n) +--R +--R +--R n +--R m (b x + a) +--R (66) (b x + a) %e +--R Type: Expression Integer +--E 66 + +--S 67 of 578 +r0013:= -(a+b*x)^(1+m)*Gamma((1+m)/n,-(a+b*x)^n)*(-(a+b*x)^n)^(-(1+m)/n)/b/n +--R +--R +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- (b x + a) ) | (-----,- (b x + a) ) +--R n +--R (67) - --------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 67 + +--S 68 of 578 +a0013:= integrate(t0013,x) +--R +--R +--R x n +--R ++ m (%A b + a) +--R (68) | (%A b + a) %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 578 +m0013:= a0013-r0013 +--R +--R +--R (69) +--R x n +--R ++ m (%A b + a) +--R b n | (%A b + a) %e d%A +--R ++ +--R + +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- (b x + a) ) | (-----,- (b x + a) ) +--R n +--R / +--R b n +--R Type: Expression Integer +--E 69 + +--S 70 of 578 +d0013:= D(m0013,x) +--R +--R +--R (70) +--R - m - 1 +--R ------- +--R m n n +--R (m + 1)(b x + a) (- (b x + a) ) +--R + +--R - n - m - 1 +--R ----------- +--R m + 1 n - 1 n n +--R (m + 1)(b x + a) (b x + a) (- (b x + a) ) +--R * +--R _ m + 1 n +--R | (-----,- (b x + a) ) +--R n +--R + +--R - n + m + 1 +--R n ----------- +--R m + 1 n - 1 (b x + a) n n +--R n (b x + a) (b x + a) %e (- (b x + a) ) +--R * +--R - m - 1 +--R ------- +--R n n +--R (- (b x + a) ) +--R + +--R n +--R m (b x + a) +--R n (b x + a) %e +--R / +--R n +--R Type: Expression Integer +--E 70 + +--S 71 of 578 +t0014:= (a+b*x)^m*f^((a+b*x)^n) +--R +--R +--R n +--R m (b x + a) +--R (71) (b x + a) f +--R Type: Expression Integer +--E 71 + +--S 72 of 578 +r0014:= -(a+b*x)^(1+m)*_ + Gamma((1+m)/n,-(a+b*x)^n*log(f))*(-(a+b*x)^n*log(f))^(-(1+m)/n)/b/n +--R +--R +--R (72) +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- log(f)(b x + a) ) | (-----,- log(f)(b x + a) ) +--R n +--R - --------------------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 72 + +--S 73 of 578 +a0014:= integrate(t0014,x) +--R +--R +--R x n +--R ++ m (%A b + a) +--R (73) | (%A b + a) f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 578 +m0014:= a0014-r0014 +--R +--R +--R (74) +--R x n +--R ++ m (%A b + a) +--R b n | (%A b + a) f d%A +--R ++ +--R + +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- log(f)(b x + a) ) | (-----,- log(f)(b x + a) ) +--R n +--R / +--R b n +--R Type: Expression Integer +--E 74 + +--S 75 of 578 +d0014:= D(m0014,x) +--R +--R +--R (75) +--R - m - 1 +--R ------- +--R m n n +--R (m + 1)(b x + a) (- log(f)(b x + a) ) +--R + +--R m + 1 n - 1 +--R (m + 1)log(f)(b x + a) (b x + a) +--R * +--R - n - m - 1 +--R ----------- +--R n n +--R (- log(f)(b x + a) ) +--R * +--R _ m + 1 n +--R | (-----,- log(f)(b x + a) ) +--R n +--R + +--R n +--R m (b x + a) +--R n (b x + a) f +--R + +--R n +--R m + 1 n - 1 log(f)(b x + a) +--R n log(f)(b x + a) (b x + a) %e +--R * +--R - n + m + 1 - m - 1 +--R ----------- ------- +--R n n n n +--R (- log(f)(b x + a) ) (- log(f)(b x + a) ) +--R / +--R n +--R Type: Expression Integer +--E 75 + +--S 76 of 578 +t0015:= exp(1)^(c+d*x)/(a+b*x)^2 +--R +--R +--R d x + c +--R %e +--R (76) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression Integer +--E 76 + +--S 77 of 578 +r0015:= -exp(1)^(c+d*x)/b/(a+b*x)+d*exp(1)^(c-a*d/b)*Ei(d*(a+b*x)/b)/b^2 +--R +--R +--R - a d + b c +--R ----------- +--R d x + c b d x + a d b +--R - b %e + (b d x + a d)Ei(-----------)%e +--R b +--R (77) --------------------------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression Integer +--E 77 + +--S 78 of 578 +a0015:= integrate(t0015,x) +--R +--R +--R x %A d + c +--R ++ %e +--R (78) | -------------------- d%A +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 578 +m0015:= a0015-r0015 +--R +--R +--R (79) +--R x %A d + c +--R 3 2 ++ %e d x + c +--R (b x + a b ) | -------------------- d%A + b %e +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R + +--R - a d + b c +--R ----------- +--R b d x + a d b +--R (- b d x - a d)Ei(-----------)%e +--R b +--R / +--R 3 2 +--R b x + a b +--R Type: Expression Integer +--E 79 + +--S 80 of 578 +d0015:= D(m0015,x) +--R +--R +--R - a d + b c b d x + a d +--R ----------- ----------- +--R b b d x + c +--R - d %e %e + d %e +--R (80) -------------------------------------------- +--R 2 +--R b x + a b +--R Type: Expression Integer +--E 80 + +--S 81 of 578 +t0016:= exp(1)^(c+d*x)/(a+b*x)^3 +--R +--R +--R d x + c +--R %e +--R (81) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression Integer +--E 81 + +--S 82 of 578 +r0016:= -1/2*exp(1)^(c+d*x)/b/(a+b*x)^2-1/2*d*_ + exp(1)^(c+d*x)/b^2/(a+b*x)+1/2*d^2*exp(1)^(c-a*d/b)*_ + Ei(d*(a+b*x)/b)/b^3 +--R +--R +--R (82) +--R 2 2 d x + c +--R (- b d x - a b d - b )%e +--R + +--R - a d + b c +--R ----------- +--R 2 2 2 2 2 2 b d x + a d b +--R (b d x + 2a b d x + a d )Ei(-----------)%e +--R b +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression Integer +--E 82 + +--S 83 of 578 +a0016:= integrate(t0016,x) +--R +--R +--R x %A d + c +--R ++ %e +--R (83) | ------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 578 +m0016:= a0016-r0016 +--R +--R +--R (84) +--R x %A d + c +--R 5 2 4 2 3 ++ %e +--R (2b x + 4a b x + 2a b ) | ------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R + +--R 2 2 d x + c +--R (b d x + a b d + b )%e +--R + +--R - a d + b c +--R ----------- +--R 2 2 2 2 2 2 b d x + a d b +--R (- b d x - 2a b d x - a d )Ei(-----------)%e +--R b +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression Integer +--E 84 + +--S 85 of 578 +d0016:= D(m0016,x) +--R +--R +--R - a d + b c b d x + a d +--R ----------- ----------- +--R 2 b b 2 d x + c +--R - d %e %e + d %e +--R (85) -------------------------------------------- +--R 3 2 +--R 2b x + 2a b +--R Type: Expression Integer +--E 85 + +--S 86 of 578 +t0017:= exp((c+d*x)^2)*(a+b*x)^2 +--R +--R +--R 2 2 2 +--R 2 2 2 d x + 2c d x + c +--R (86) (b x + 2a b x + a )%e +--R Type: Expression Integer +--E 86 + +--S 87 of 578 +r0017:= -b*(1/2*b*c-a*d)*_ + exp((c+d*x)^2)/d^3+1/2*b^2*_ + exp((c+d*x)^2)*x/d^2-1/4*(b^2*(1-2*c^2)+4*a*b*c*d-2*a^2*d^2)*_ + %pi^(1/2)*erfi(c+d*x)/d^3 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 578 +a0017:= integrate(t0017,x) +--R +--R +--R x 2 2 2 +--R ++ 2 2 2 %A d + 2%A c d + c +--R (87) | (%A b + 2%A a b + a )%e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 578 +m0017:= a0017-r0017 +--R +--R +--R x 2 2 2 +--R ++ 2 2 2 %A d + 2%A c d + c +--R (88) | (%A b + 2%A a b + a )%e d%A - r0017 +--R ++ +--R Type: Expression Integer +--E 89 + +--S 90 of 578 +d0017:= D(m0017,x) +--R +--R +--R 2 2 2 +--R 2 2 2 d x + 2c d x + c +--R (89) (b x + 2a b x + a )%e +--R Type: Expression Integer +--E 90 + +--S 91 of 578 +t0018:= exp((c+d*x)^3)*(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R 2 2 2 d x + 3c d x + 3c d x + c +--R (90) (b x + 2a b x + a )%e +--R Type: Expression Integer +--E 91 + +--S 92 of 578 +r0018:= 1/3*b^2*exp((c+d*x)^3)/d^3-1/3*(b*c-a*d)^2*(c+d*x)*_ + Gamma(1/3,-(c+d*x)^3)/d^3/(-(c+d*x)^3)^(1/3)+_ + 2/3*b*(b*c-a*d)*(c+d*x)^2*_ + Gamma(2/3,-(c+d*x)^3)/d^3/(-(c+d*x)^3)^(2/3) +--R +--R +--R (91) +--R 3 3 2 2 2 3 +------------------------------+2 +--R 2 d x + 3c d x + 3c d x + c 3| 3 3 2 2 2 3 +--R b %e \|- d x - 3c d x - 3c d x - c +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- a d + 2a b c d - b c d)x - a c d + 2a b c d - b c ) +--R * +--R +------------------------------+ +--R _ 1 3 3 2 2 2 3 3| 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c )\|- d x - 3c d x - 3c d x - c +--R 3 +--R + +--R 3 2 2 2 2 2 2 2 2 3 +--R ((- 2a b d + 2b c d )x + (- 4a b c d + 4b c d)x - 2a b c d + 2b c ) +--R * +--R _ 2 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression Integer +--E 92 + +--S 93 of 578 +a0018:= integrate(t0018,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ 2 2 2 %A d + 3%A c d + 3%A c d + c +--R (92) | (%A b + 2%A a b + a )%e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 578 +m0018:= a0018-r0018 +--R +--R +--R (93) +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R * +--R x 3 3 2 2 2 3 +--R ++ 2 2 2 %A d + 3%A c d + 3%A c d + c +--R | (%A b + 2%A a b + a )%e d%A +--R ++ +--R + +--R 3 3 2 2 2 3 +------------------------------+2 +--R 2 d x + 3c d x + 3c d x + c 3| 3 3 2 2 2 3 +--R - b %e \|- d x - 3c d x - 3c d x - c +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((a d - 2a b c d + b c d)x + a c d - 2a b c d + b c ) +--R * +--R +------------------------------+ +--R _ 1 3 3 2 2 2 3 3| 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c )\|- d x - 3c d x - 3c d x - c +--R 3 +--R + +--R 3 2 2 2 2 2 2 2 2 3 +--R ((2a b d - 2b c d )x + (4a b c d - 4b c d)x + 2a b c d - 2b c ) +--R * +--R _ 2 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression Integer +--E 94 + +--S 95 of 578 +d0018:= D(m0018,x) +--R +--R +--R (94) 0 +--R Type: Expression Integer +--E 95 + +--S 96 of 578 +t0019:= exp((c+d*x)^3)*(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (95) (b x + a)%e +--R Type: Expression Integer +--E 96 + +--S 97 of 578 +r0019:= 1/3*(b*c-a*d)*(c+d*x)*_ + Gamma(1/3,-(c+d*x)^3)/d^2/(-(c+d*x)^3)^(1/3)-_ + 1/3*b*(c+d*x)^2*_ + Gamma(2/3,-(c+d*x)^3)/d^2/(-(c+d*x)^3)^(2/3) +--R +--R +--R (96) +--R 2 2 _ 1 3 3 2 2 2 3 +--R ((- a d + b c d)x - a c d + b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- d x - 3c d x - 3c d x - c +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (- b d x - 2b c d x - b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression Integer +--E 97 + +--S 98 of 578 +a0019:= integrate(t0019,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A d + 3%A c d + 3%A c d + c +--R (97) | (%A b + a)%e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 578 +m0019:= a0019-r0019 +--R +--R +--R (98) +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R * +--R x 3 3 2 2 2 3 +--R ++ %A d + 3%A c d + 3%A c d + c +--R | (%A b + a)%e d%A +--R ++ +--R + +--R 2 2 _ 1 3 3 2 2 2 3 +--R ((a d - b c d)x + a c d - b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- d x - 3c d x - 3c d x - c +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (b d x + 2b c d x + b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression Integer +--E 99 + +--S 100 of 578 +d0019:= D(m0019,x) +--R +--R +--R (99) 0 +--R Type: Expression Integer +--E 100 + +--S 101 of 578 +t0020:= x^2*exp(1)^(a+b*x)/(c+d*x^2) +--R +--R +--R 2 b x + a +--R x %e +--R (100) ----------- +--R 2 +--R d x + c +--R Type: Expression Integer +--E 101 + +--S 102 of 578 +r0020:= exp(1)^(a+b*x)/b/d-1/2*c^(1/2)*_ + exp(1)^(a+b*c^(1/2)/(-d)^(1/2))*_ + Ei(-b*(c^(1/2)-(-d)^(1/2)*x)/(-d)^(1/2))/(-d)^(3/2)+1/2*c^(1/2)*_ + exp(1)^(a-b*c^(1/2)/(-d)^(1/2))*_ + Ei(b*(c^(1/2)+(-d)^(1/2)*x)/(-d)^(1/2))/(-d)^(3/2) +--R +--R +--R (101) +--R +-+ +---+ +--R b\|c + a\|- d +--R --------------- +--R +-+ +---+ +---+ +--R +-+ - b\|c + b x\|- d \|- d +--R b\|c Ei(-------------------)%e +--R +---+ +--R \|- d +--R + +--R +-+ +---+ +--R - b\|c + a\|- d +--R ----------------- +--R +-+ +---+ +---+ +--R +-+ b\|c + b x\|- d \|- d b x + a +---+ +--R - b\|c Ei(-----------------)%e + 2%e \|- d +--R +---+ +--R \|- d +--R / +--R +---+ +--R 2b d\|- d +--R Type: Expression Integer +--E 102 + +--S 103 of 578 +a0020:= integrate(t0020,x) +--R +--R +--R x 2 %A b + a +--R ++ %A %e +--R (102) | ------------- d%A +--R ++ 2 +--R %A d + c +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 578 +m0020:= a0020-r0020 +--R +--R +--R (103) +--R x 2 %A b + a +--R +---+ ++ %A %e +--R 2b d\|- d | ------------- d%A +--R ++ 2 +--R %A d + c +--R + +--R +-+ +---+ +--R b\|c + a\|- d +--R --------------- +--R +-+ +---+ +---+ +--R +-+ - b\|c + b x\|- d \|- d +--R - b\|c Ei(-------------------)%e +--R +---+ +--R \|- d +--R + +--R +-+ +---+ +--R - b\|c + a\|- d +--R ----------------- +--R +-+ +---+ +---+ +--R +-+ b\|c + b x\|- d \|- d b x + a +---+ +--R b\|c Ei(-----------------)%e - 2%e \|- d +--R +---+ +--R \|- d +--R / +--R +---+ +--R 2b d\|- d +--R Type: Expression Integer +--E 104 + +--S 105 of 578 +d0020:= D(m0020,x) +--R +--R +--R (104) +--R +-+ +---+ +-+ +---+ +--R - b\|c + a\|- d b\|c + b x\|- d +--R ----------------- ----------------- +--R +---+ +---+ +--R +---+ +-+ \|- d \|- d +--R (- x\|- d \|c + c)%e %e +--R + +--R +-+ +---+ +-+ +---+ +--R - b\|c + b x\|- d b\|c + a\|- d +--R ------------------- --------------- +--R +---+ +---+ +--R +---+ +-+ \|- d \|- d b x + a +--R (x\|- d \|c + c)%e %e - 2c %e +--R / +--R 2 2 +--R 2d x + 2c d +--R Type: Expression Integer +--E 105 + +--S 106 of 578 +t0021:= 1/(a+b*exp(1)^(c-d*x)) +--R +--R +--R 1 +--R (105) ----------------- +--R - d x + c +--R b %e + a +--R Type: Expression Integer +--E 106 + +--S 107 of 578 +r0021:= log(b+a*exp(-c+d*x))/a/d +--R +--R +--R d x - c +--R log(a %e + b) +--R (106) -------------------- +--R a d +--R Type: Expression Integer +--E 107 + +--S 108 of 578 +a0021:= integrate(t0021,x) +--R +--R +--R - d x + c +--R log(b %e + a) + d x +--R (107) ---------------------------- +--R a d +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 578 +m0021:= a0021-r0021 +--R +--R +--R d x - c - d x + c +--R - log(a %e + b) + log(b %e + a) + d x +--R (108) ----------------------------------------------------- +--R a d +--R Type: Expression Integer +--E 109 + +--S 110 of 578 +d0021:= D(m0021,x) +--R +--R +--R - d x + c d x - c +--R - b %e %e + b +--R (109) ----------------------------------------------------- +--R - d x + c 2 d x - c 2 - d x + c +--R (a b %e + a )%e + b %e + a b +--R Type: Expression Integer +--E 110 + +--S 111 of 578 +t0022:= 1/(a+b*exp(1)^(c-d*x))^2 +--R +--R +--R 1 +--R (110) ---------------------------------------- +--R 2 - d x + c 2 - d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 111 + +--S 112 of 578 +r0022:= -1/a/d/(a+b*exp(1)^(c-d*x))+log(b+a*exp(1)^(-c+d*x))/a^2/d +--R +--R +--R - d x + c d x - c +--R (b %e + a)log(a %e + b) - a +--R (111) ------------------------------------------- +--R 2 - d x + c 3 +--R a b d %e + a d +--R Type: Expression Integer +--E 112 + +--S 113 of 578 +a0022:= integrate(t0022,x) +--R +--R +--R (112) +--R - d x + c - d x + c - d x + c +--R (b %e + a)log(b %e + a) + b d x %e + a d x - a +--R ------------------------------------------------------------------------- +--R 2 - d x + c 3 +--R a b d %e + a d +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 578 +m0022:= a0022-r0022 +--R +--R +--R d x - c - d x + c +--R - log(a %e + b) + log(b %e + a) + d x +--R (113) ----------------------------------------------------- +--R 2 +--R a d +--R Type: Expression Integer +--E 114 + +--S 115 of 578 +d0022:= D(m0022,x) +--R +--R +--R - d x + c d x - c +--R - b %e %e + b +--R (114) ------------------------------------------------------- +--R 2 - d x + c 3 d x - c 2 - d x + c 2 +--R (a b %e + a )%e + a b %e + a b +--R Type: Expression Integer +--E 115 + +--S 116 of 578 +t0023:= 1/(a+b*exp(1)^(-c-d*x)) +--R +--R +--R 1 +--R (115) ----------------- +--R - d x - c +--R b %e + a +--R Type: Expression Integer +--E 116 + +--S 117 of 578 +r0023:= log(b+a*exp(c+d*x))/a/d +--R +--R +--R d x + c +--R log(a %e + b) +--R (116) -------------------- +--R a d +--R Type: Expression Integer +--E 117 + +--S 118 of 578 +a0023:= integrate(t0023,x) +--R +--R +--R - d x - c +--R log(b %e + a) + d x +--R (117) ---------------------------- +--R a d +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 578 +m0023:= a0023-r0023 +--R +--R +--R d x + c - d x - c +--R - log(a %e + b) + log(b %e + a) + d x +--R (118) ----------------------------------------------------- +--R a d +--R Type: Expression Integer +--E 119 + +--S 120 of 578 +d0023:= D(m0023,x) +--R +--R +--R - d x - c d x + c +--R - b %e %e + b +--R (119) ----------------------------------------------------- +--R - d x - c 2 d x + c 2 - d x - c +--R (a b %e + a )%e + b %e + a b +--R Type: Expression Integer +--E 120 + +--S 121 of 578 +t0024:= 1/(a+b*exp(1)^(-c-d*x))^2 +--R +--R +--R 1 +--R (120) ---------------------------------------- +--R 2 - d x - c 2 - d x - c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 121 + +--S 122 of 578 +r0024:= -1/a/d/(a+b*exp(1)^(-c-d*x))+log(b+a*exp(1)^(c+d*x))/a^2/d +--R +--R +--R - d x - c d x + c +--R (b %e + a)log(a %e + b) - a +--R (121) ------------------------------------------- +--R 2 - d x - c 3 +--R a b d %e + a d +--R Type: Expression Integer +--E 122 + +--S 123 of 578 +a0024:= integrate(t0024,x) +--R +--R +--R (122) +--R - d x - c - d x - c - d x - c +--R (b %e + a)log(b %e + a) + b d x %e + a d x - a +--R ------------------------------------------------------------------------- +--R 2 - d x - c 3 +--R a b d %e + a d +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 578 +m0024:= a0024-r0024 +--R +--R +--R d x + c - d x - c +--R - log(a %e + b) + log(b %e + a) + d x +--R (123) ----------------------------------------------------- +--R 2 +--R a d +--R Type: Expression Integer +--E 124 + +--S 125 of 578 +d0024:= D(m0024,x) +--R +--R +--R - d x - c d x + c +--R - b %e %e + b +--R (124) ------------------------------------------------------- +--R 2 - d x - c 3 d x + c 2 - d x - c 2 +--R (a b %e + a )%e + a b %e + a b +--R Type: Expression Integer +--E 125 + +--S 126 of 578 +t0025:= 1/(a+b*exp(1)^(-c-d*x))^3 +--R +--R +--R 1 +--R (125) -------------------------------------------------------------- +--R 3 - d x - c 3 2 - d x - c 2 2 - d x - c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 126 + +--S 127 of 578 +r0025:= -1/2/a/d/(a+b*exp(1)^(-c-d*x))^2-1/a^2/d/(a+b*exp(1)^(-c-d*x))+_ + log(b+a*exp(1)^(c+d*x))/a^3/d +--R +--R +--R (126) +--R 2 - d x - c 2 - d x - c 2 d x + c +--R (2b (%e ) + 4a b %e + 2a )log(a %e + b) +--R + +--R - d x - c 2 +--R - 2a b %e - 3a +--R / +--R 3 2 - d x - c 2 4 - d x - c 5 +--R 2a b d (%e ) + 4a b d %e + 2a d +--R Type: Expression Integer +--E 127 + +--S 128 of 578 +a0025:= integrate(t0025,x) +--R +--R +--R (127) +--R 2 - d x - c 2 - d x - c 2 - d x - c +--R (2b (%e ) + 4a b %e + 2a )log(b %e + a) +--R + +--R 2 - d x - c 2 - d x - c 2 2 +--R 2b d x (%e ) + (4a b d x - 2a b)%e + 2a d x - 3a +--R / +--R 3 2 - d x - c 2 4 - d x - c 5 +--R 2a b d (%e ) + 4a b d %e + 2a d +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 578 +m0025:= a0025-r0025 +--R +--R +--R d x + c - d x - c +--R - log(a %e + b) + log(b %e + a) + d x +--R (128) ----------------------------------------------------- +--R 3 +--R a d +--R Type: Expression Integer +--E 129 + +--S 130 of 578 +d0025:= D(m0025,x) +--R +--R +--R - d x - c d x + c +--R - b %e %e + b +--R (129) ------------------------------------------------------- +--R 3 - d x - c 4 d x + c 2 2 - d x - c 3 +--R (a b %e + a )%e + a b %e + a b +--R Type: Expression Integer +--E 130 + +--S 131 of 578 +t0026:= x/(a+b*exp(1)^(c+d*x)) +--R +--R +--R x +--R (130) --------------- +--R d x + c +--R b %e + a +--R Type: Expression Integer +--E 131 + +--S 132 of 578 +r0026:= -1/2*(-d^2*x^2+2*x*log((a+b*exp(c+d*x))/a)*d+2*_ + polylog(2,-b*exp(c+d*x)/a))/a/d^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 578 +a0026:= integrate(t0026,x) +--R +--R +--R x +--R ++ %A +--R (131) | ---------------- d%A +--R ++ %A d + c +--R b %e + a +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 578 +m0026:= a0026-r0026 +--R +--R +--R x +--R ++ %A +--R (132) | ---------------- d%A - r0026 +--R ++ %A d + c +--R b %e + a +--R Type: Expression Integer +--E 134 + +--S 135 of 578 +d0026:= D(m0026,x) +--R +--R +--R x +--R (133) --------------- +--R d x + c +--R b %e + a +--R Type: Expression Integer +--E 135 + +--S 136 of 578 +t0027:= x^2/(a+b*exp(1)^(c+d*x)) +--R +--R +--R 2 +--R x +--R (134) --------------- +--R d x + c +--R b %e + a +--R Type: Expression Integer +--E 136 + +--S 137 of 578 +r0027:= 1/3*(d^3*x^3-3*x^2*log((a+b*exp(c+d*x))/a)*d^2-6*x*_ + polylog(2,-b*exp(c+d*x)/a)*d+6*_ + polylog(3,-b*exp(c+d*x)/a))/a/d^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 578 +a0027:= integrate(t0027,x) +--R +--R +--R x 2 +--R ++ %A +--R (135) | ---------------- d%A +--R ++ %A d + c +--R b %e + a +--R Type: Union(Expression Integer,...) +--E 138 + +--S 139 of 578 +m0027:= a0027-r0027 +--R +--R +--R x 2 +--R ++ %A +--R (136) | ---------------- d%A - r0027 +--R ++ %A d + c +--R b %e + a +--R Type: Expression Integer +--E 139 + +--S 140 of 578 +d0027:= D(m0027,x) +--R +--R +--R 2 +--R x +--R (137) --------------- +--R d x + c +--R b %e + a +--R Type: Expression Integer +--E 140 + +--S 141 of 578 +t0028:= x^3/(a+b*exp(1)^(c+d*x)) +--R +--R +--R 3 +--R x +--R (138) --------------- +--R d x + c +--R b %e + a +--R Type: Expression Integer +--E 141 + +--S 142 of 578 +r0028:= 1/4*(x^4*d^4-4*x^3*log((a+b*exp(c+d*x))/a)*d^3-12*x^2*_ + polylog(2,-b*exp(c+d*x)/a)*d^2+24*x*_ + polylog(3,-b*exp(c+d*x)/a)*d-24*_ + polylog(4,-b*exp(c+d*x)/a))/a/d^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 578 +a0028:= integrate(t0028,x) +--R +--R +--R x 3 +--R ++ %A +--R (139) | ---------------- d%A +--R ++ %A d + c +--R b %e + a +--R Type: Union(Expression Integer,...) +--E 143 + +--S 144 of 578 +m0028:= a0028-r0028 +--R +--R +--R x 3 +--R ++ %A +--R (140) | ---------------- d%A - r0028 +--R ++ %A d + c +--R b %e + a +--R Type: Expression Integer +--E 144 + +--S 145 of 578 +d0028:= D(m0028,x) +--R +--R +--R 3 +--R x +--R (141) --------------- +--R d x + c +--R b %e + a +--R Type: Expression Integer +--E 145 + +--S 146 of 578 +t0029:= x/(a+b*exp(1)^(c+d*x))^2 +--R +--R +--R x +--R (142) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 146 + +--S 147 of 578 +r0029:= -x/a^2/d+x/a/d/(a+b*exp(1)^(c+d*x))+1/2*x^2/a^2+_ + log(a+b*exp(1)^(c+d*x))/a^2/d^2-_ + x*log(1+b*exp(1)^(c+d*x)/a)/a^2/d-_ + polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 578 +a0029:= integrate(t0029,x) +--R +--R +--R x +--R ++ %A +--R (143) | -------------------------------------- d%A +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Union(Expression Integer,...) +--E 148 + +--S 149 of 578 +m0029:= a0029-r0029 +--R +--R +--R x +--R ++ %A +--R (144) | -------------------------------------- d%A - r0029 +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 149 + +--S 150 of 578 +d0029:= D(m0029,x) +--R +--R +--R x +--R (145) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 150 + +--S 151 of 578 +t0030:= x^2/(a+b*exp(1)^(c+d*x))^2 +--R +--R +--R 2 +--R x +--R (146) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 151 + +--S 152 of 578 +r0030:= -x^2/a^2/d+x^2/a/d/(a+b*exp(1)^(c+d*x))+_ + 1/3*x^3/a^2+2*x*log(1+b*exp(1)^(c+d*x)/a)/a^2/d^2-_ + x^2*log(1+b*exp(1)^(c+d*x)/a)/a^2/d+_ + 2*(1-d*x)*polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^3+_ + 2*polylog(3,-b*exp(1)^(c+d*x)/a)/a^2/d^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 578 +a0030:= integrate(t0030,x) +--R +--R +--R x 2 +--R ++ %A +--R (147) | -------------------------------------- d%A +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Union(Expression Integer,...) +--E 153 + +--S 154 of 578 +m0030:= a0030-r0030 +--R +--R +--R x 2 +--R ++ %A +--R (148) | -------------------------------------- d%A - r0030 +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 154 + +--S 155 of 578 +d0030:= D(m0030,x) +--R +--R +--R 2 +--R x +--R (149) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 155 + +--S 156 of 578 +t0031:= x^3/(a+b*exp(1)^(c+d*x))^2 +--R +--R +--R 3 +--R x +--R (150) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 156 + +--S 157 of 578 +r0031:= -x^3/a^2/d+x^3/a/d/(a+b*exp(1)^(c+d*x))+1/4*x^4/a^2+_ + 3*x^2*log(1+b*exp(1)^(c+d*x)/a)/a^2/d^2-_ + x^3*log(1+b*exp(1)^(c+d*x)/a)/a^2/d+3*x*(2-d*x)*_ + polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^3-6*(1-d*x)*_ + polylog(3,-b*exp(1)^(c+d*x)/a)/a^2/d^4-6*_ + polylog(4,-b*exp(1)^(c+d*x)/a)/a^2/d^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 578 +a0031:= integrate(t0031,x) +--R +--R +--R x 3 +--R ++ %A +--R (151) | -------------------------------------- d%A +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 578 +m0031:= a0031-r0031 +--R +--R +--R x 3 +--R ++ %A +--R (152) | -------------------------------------- d%A - r0031 +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 159 + +--S 160 of 578 +d0031:= D(m0031,x) +--R +--R +--R 3 +--R x +--R (153) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression Integer +--E 160 + +--S 161 of 578 +t0032:= x/(a+b*exp(1)^(c+d*x))^3 +--R +--R +--R x +--R (154) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 161 + +--S 162 of 578 +r0032:= -1/2/a^2/d^2/(a+b*exp(1)^(c+d*x))-3/2*x/a^3/d+1/2*x^2/a^3+_ + 1/2*x*(2*a/d/(a+b*exp(1)^(c+d*x))+(a^2/(a+b*exp(1)^(c+d*x))^2-_ + 2*log(a+b*exp(1)^(c+d*x)))/d)/a^3+3/2*_ + log(a+b*exp(1)^(c+d*x))/a^3/d^2+x*_ + log(a+b*exp(1)^(c+d*x))/a^3/d-x*log(1+b*exp(1)^(c+d*x)/a)/a^3/d-_ + polylog(2,-b*exp(1)^(c+d*x)/a)/a^3/d^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 578 +a0032:= integrate(t0032,x) +--R +--R +--R (155) +--R x +--R ++ %A +--R | ----------------------------------------------------------- d%A +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 578 +m0032:= a0032-r0032 +--R +--R +--R (156) +--R x +--R ++ %A +--R | ----------------------------------------------------------- d%A - r0032 +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 164 + +--S 165 of 578 +d0032:= D(m0032,x) +--R +--R +--R x +--R (157) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 165 + +--S 166 of 578 +t0033:= x^2/(a+b*exp(1)^(c+d*x))^3 +--R +--R +--R 2 +--R x +--R (158) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 166 + +--S 167 of 578 +r0033:= x/a^3/d^2-x/a^2/d^2/(a+b*exp(1)^(c+d*x))-3/2*x^2/a^3/d+1/3*x^3/a^3+_ + 1/2*x^2*(2*a/d/(a+b*exp(1)^(c+d*x))+(a^2/(a+b*exp(1)^(c+d*x))^2-_ + 2*log(a+b*exp(1)^(c+d*x)))/d)/a^3-log(a+b*exp(1)^(c+d*x))/a^3/d^3+_ + x^2*log(a+b*exp(1)^(c+d*x))/a^3/d+3*x*_ + log(1+b*exp(1)^(c+d*x)/a)/a^3/d^2-x^2*log(1+b*exp(1)^(c+d*x)/a)/a^3/d+_ + (3-2*d*x)*polylog(2,-b*exp(1)^(c+d*x)/a)/a^3/d^3+2*_ + polylog(3,-b*exp(1)^(c+d*x)/a)/a^3/d^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 578 +a0033:= integrate(t0033,x) +--R +--R +--R (159) +--R x 2 +--R ++ %A +--R | ----------------------------------------------------------- d%A +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 578 +m0033:= a0033-r0033 +--R +--R +--R (160) +--R x 2 +--R ++ %A +--R | ----------------------------------------------------------- d%A - r0033 +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 169 + +--S 170 of 578 +d0033:= D(m0033,x) +--R +--R +--R 2 +--R x +--R (161) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression Integer +--E 170 + +--S 171 of 578 +t0034:= (exp(1)^(a+b*x))^(1/2)/x +--R +--R +--R +---------+ +--R | b x + a +--R \|%e +--R (162) ------------ +--R x +--R Type: Expression Integer +--E 171 + +--S 172 of 578 +r0034:= exp(a+b*x)^(1/2)*Ei(1/2*b*x)*exp(-1/2*b*x) +--R +--R +--R b x +--R - --- +---------+ +--R b x 2 | b x + a +--R (163) Ei(---)%e \|%e +--R 2 +--R Type: Expression Integer +--E 172 + +--S 173 of 578 +a0034:= integrate(t0034,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 578 +m0034:= a0034-r0034 +--R +--R +--R b x +--R - --- +---------+ +--R b x 2 | b x + a +--R (164) - Ei(---)%e \|%e + a0034 +--R 2 +--R Type: Expression Integer +--E 174 + +--S 175 of 578 +d0034:= D(m0034,x) +--R +--R +--R b x b x +--R - --- --- +---------+ +--R 2 2 | b x + a +--R %e %e \|%e +--R (165) - ------------------------ +--R x +--R Type: Expression Integer +--E 175 + +--S 176 of 578 +t0035:= (exp(1)^(a+b*x))^(1/2)/x^2 +--R +--R +--R +---------+ +--R | b x + a +--R \|%e +--R (166) ------------ +--R 2 +--R x +--R Type: Expression Integer +--E 176 + +--S 177 of 578 +r0035:= 1/2*exp(-1/2*a-1/2*b*x)*exp(a+b*x)^(1/2)*(-2*exp(1/2*a+1/2*b*x)+_ + b*exp(1/2*a)*Ei(1/2*b*x)*x)/x +--R +--R +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 b x 2 2 | b x + a +--R (- 2%e %e + b x Ei(---)%e %e )\|%e +--R 2 +--R (167) ----------------------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 177 + +--S 178 of 578 +a0035:= integrate(t0035,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 178 + +--S 179 of 578 +m0035:= a0035-r0035 +--R +--R +--R (168) +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 b x 2 2 | b x + a +--R (2%e %e - b x Ei(---)%e %e )\|%e + 2a0035 x +--R 2 +--R -------------------------------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 179 + +--S 180 of 578 +d0035:= D(m0035,x) +--R +--R +--R - b x - a b x + a - b x - a a b x +--R --------- ------- --------- - --- +--R 2 2 2 2 2 b x + a +--R ((b x - 2)%e %e - b x %e %e %e )%e +--R (169) ------------------------------------------------------------------ +--R +---------+ +--R 2 | b x + a +--R 2x \|%e +--R Type: Expression Integer +--E 180 + +--S 181 of 578 +t0036:= (exp(1)^(a+b*x))^(1/2)/x^3 +--R +--R +--R +---------+ +--R | b x + a +--R \|%e +--R (170) ------------ +--R 3 +--R x +--R Type: Expression Integer +--E 181 + +--S 182 of 578 +r0036:= 1/8*exp(-1/2*a-1/2*b*x)*exp(a+b*x)^(1/2)*(-4*exp(1/2*a+1/2*b*x)-_ + 2*b*exp(1/2*a+1/2*b*x)*x+b^2*exp(1/2*a)*Ei(1/2*b*x)*x^2)/x^2 +--R +--R +--R (171) +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 2 2 b x 2 2 | b x + a +--R ((- 2b x - 4)%e %e + b x Ei(---)%e %e )\|%e +--R 2 +--R -------------------------------------------------------------------------- +--R 2 +--R 8x +--R Type: Expression Integer +--E 182 + +--S 183 of 578 +a0036:= integrate(t0036,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 183 + +--S 184 of 578 +m0036:= a0036-r0036 +--R +--R +--R (172) +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 2 2 b x 2 2 | b x + a +--R ((2b x + 4)%e %e - b x Ei(---)%e %e )\|%e +--R 2 +--R + +--R 2 +--R 8a0036 x +--R / +--R 2 +--R 8x +--R Type: Expression Integer +--E 184 + +--S 185 of 578 +d0036:= D(m0036,x) +--R +--R +--R - b x - a b x + a - b x - a a b x +--R --------- ------- --------- - --- +--R 2 2 2 2 2 2 2 2 2 b x + a +--R ((b x - 8)%e %e - b x %e %e %e )%e +--R (173) ------------------------------------------------------------------- +--R +---------+ +--R 3 | b x + a +--R 8x \|%e +--R Type: Expression Integer +--E 185 + +--S 186 of 578 +t0037:= f^(a+b*(c+d*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R (174) f +--R Type: Expression Integer +--E 186 + +--S 187 of 578 +r0037:= -1/3*f^a*(c+d*x)*Gamma(1/3,-b*(c+d*x)^3*log(f))/d/_ + (-b*(c+d*x)^3*log(f))^(1/3) +--R +--R +--R a _ 1 3 3 2 2 2 3 +--R (- d x - c)f | (-,(- b d x - 3b c d x - 3b c d x - b c )log(f)) +--R 3 +--R (175) ----------------------------------------------------------------- +--R +----------------------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3d\|(- b d x - 3b c d x - 3b c d x - b c )log(f) +--R Type: Expression Integer +--E 187 + +--S 188 of 578 +a0037:= integrate(t0037,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b d + 3%A b c d + 3%A b c d + b c + a +--R (176) | f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 188 + +--S 189 of 578 +m0037:= a0037-r0037 +--R +--R +--R (177) +--R +----------------------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3d\|(- b d x - 3b c d x - 3b c d x - b c )log(f) +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b d + 3%A b c d + 3%A b c d + b c + a +--R | f d%A +--R ++ +--R + +--R a _ 1 3 3 2 2 2 3 +--R (d x + c)f | (-,(- b d x - 3b c d x - 3b c d x - b c )log(f)) +--R 3 +--R / +--R +----------------------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3d\|(- b d x - 3b c d x - 3b c d x - b c )log(f) +--R Type: Expression Integer +--E 189 + +--S 190 of 578 +d0037:= D(m0037,x) +--R +--R +--R (178) +--R 3 3 2 2 2 3 +--R a (b d x + 3b c d x + 3b c d x + b c )log(f) +--R - f %e +--R + +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R f +--R Type: Expression Integer +--E 190 + +--S 191 of 578 +t0038:= f^(a+b*(c+d*x)^n) +--R +--R +--R n +--R b (d x + c) + a +--R (179) f +--R Type: Expression Integer +--E 191 + +--S 192 of 578 +r0038:= -f^a*(c+d*x)*Gamma(1/n,-b*(c+d*x)^n*log(f))/_ + ((-b*(c+d*x)^n*log(f))^(1/n))/d/n +--R +--R +--R a _ 1 n +--R (- d x - c)f | (-,- b log(f)(d x + c) ) +--R n +--R (180) --------------------------------------- +--R 1 +--R - +--R n n +--R d n (- b log(f)(d x + c) ) +--R Type: Expression Integer +--E 192 + +--S 193 of 578 +a0038:= integrate(t0038,x) +--R +--R +--R x n +--R ++ b (%A d + c) + a +--R (181) | f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 193 + +--S 194 of 578 +m0038:= a0038-r0038 +--R +--R +--R (182) +--R 1 +--R - x n +--R n n ++ b (%A d + c) + a +--R d n (- b log(f)(d x + c) ) | f d%A +--R ++ +--R + +--R a _ 1 n +--R (d x + c)f | (-,- b log(f)(d x + c) ) +--R n +--R / +--R 1 +--R - +--R n n +--R d n (- b log(f)(d x + c) ) +--R Type: Expression Integer +--E 194 + +--S 195 of 578 +d0038:= D(m0038,x) +--R +--R +--R (183) +--R 1 +--R - +--R a n n +--R f (- b log(f)(d x + c) ) +--R + +--R - n + 1 +--R ------- +--R a n - 1 n n +--R (b d x + b c)log(f)f (d x + c) (- b log(f)(d x + c) ) +--R * +--R _ 1 n +--R | (-,- b log(f)(d x + c) ) +--R n +--R + +--R 1 2 +--R - n +--R n n b (d x + c) + a +--R n ((- b log(f)(d x + c) ) ) f +--R + +--R n +--R a n - 1 b log(f)(d x + c) +--R (b d n x + b c n)log(f)f (d x + c) %e +--R * +--R - n + 1 1 +--R ------- - +--R n n n n +--R (- b log(f)(d x + c) ) (- b log(f)(d x + c) ) +--R / +--R 1 2 +--R - +--R n n +--R n ((- b log(f)(d x + c) ) ) +--R Type: Expression Integer +--E 195 + +--S 196 of 578 +t0039:= f^(a+b*(c+d*x)^(1/2)) +--R +--R +--R +-------+ +--R b\|d x + c + a +--R (184) f +--R Type: Expression Integer +--E 196 + +--S 197 of 578 +r0039:= 2*f^(a+b*(c+d*x)^(1/2))*(-1+(c+d*x)^(1/2)*b*log(f))/b^2/d/log(f)^2 +--R +--R +--R +-------+ +--R +-------+ b\|d x + c + a +--R (2b log(f)\|d x + c - 2)f +--R (185) ----------------------------------------- +--R 2 2 +--R b d log(f) +--R Type: Expression Integer +--E 197 + +--S 198 of 578 +a0039:= integrate(t0039,x) +--R +--R +--R +-------+ +--R +-------+ b log(f)\|d x + c + a log(f) +--R (2b log(f)\|d x + c - 2)%e +--R (186) -------------------------------------------------------- +--R 2 2 +--R b d log(f) +--R Type: Union(Expression Integer,...) +--E 198 + +--S 199 of 578 +m0039:= a0039-r0039 +--R +--R +--R (187) +--R +-------+ +--R +-------+ b\|d x + c + a +--R (- 2b log(f)\|d x + c + 2)f +--R + +--R +-------+ +--R +-------+ b log(f)\|d x + c + a log(f) +--R (2b log(f)\|d x + c - 2)%e +--R / +--R 2 2 +--R b d log(f) +--R Type: Expression Integer +--E 199 + +--S 200 of 578 +d0039:= D(m0039,x) +--R +--R +--R +-------+ +-------+ +--R b\|d x + c + a b log(f)\|d x + c + a log(f) +--R (188) - f + %e +--R Type: Expression Integer +--E 200 + +--S 201 of 578 +t0040:= f^(a+b*(c+d*x)^(1/3)) +--R +--R +--R 3+-------+ +--R b\|d x + c + a +--R (189) f +--R Type: Expression Integer +--E 201 + +--S 202 of 578 +r0040:= 3*f^(a+b*(c+d*x)^(1/3))*(2-2*(c+d*x)^(1/3)*b*log(f)+_ + (c+d*x)^(2/3)*b^2*log(f)^2)/b^3/d/log(f)^3 +--R +--R +--R 3+-------+ +--R 2 2 3+-------+2 3+-------+ b\|d x + c + a +--R (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6)f +--R (190) ----------------------------------------------------------------- +--R 3 3 +--R b d log(f) +--R Type: Expression Integer +--E 202 + +--S 203 of 578 +a0040:= integrate(t0040,x) +--R +--R +--R (191) +--R 2 2 3+-------+2 3+-------+ +--R (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6) +--R * +--R 3+-------+ +--R b log(f)\|d x + c + a log(f) +--R %e +--R / +--R 3 3 +--R b d log(f) +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 578 +m0040:= a0040-r0040 +--R +--R +--R (192) +--R 3+-------+ +--R 2 2 3+-------+2 3+-------+ b\|d x + c + a +--R (- 3b log(f) \|d x + c + 6b log(f)\|d x + c - 6)f +--R + +--R 2 2 3+-------+2 3+-------+ +--R (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6) +--R * +--R 3+-------+ +--R b log(f)\|d x + c + a log(f) +--R %e +--R / +--R 3 3 +--R b d log(f) +--R Type: Expression Integer +--E 204 + +--S 205 of 578 +d0040:= D(m0040,x) +--R +--R +--R 3+-------+ 3+-------+ +--R b\|d x + c + a b log(f)\|d x + c + a log(f) +--R (193) - f + %e +--R Type: Expression Integer +--E 205 + +--S 206 of 578 +t0041:= x^3*exp(1)^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (194) x %e +--R Type: Expression Integer +--E 206 + +--S 207 of 578 +r0041:= 1/8*b^2*exp(1)^(a+b*x+c*x^2)/c^3-1/2*exp(1)^(a+b*x+c*x^2)/c^2-_ + 1/4*b*exp(1)^(a+b*x+c*x^2)*x/c^2+1/2*exp(1)^(a+b*x+c*x^2)*x^2/c-_ + 1/16*b*(b^2-6*c)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)/c^(1/2))/c^(7/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 578 +a0041:= integrate(t0041,x) +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (195) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 208 + +--S 209 of 578 +m0041:= a0041-r0041 +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (196) | %A %e d%A - r0041 +--R ++ +--R Type: Expression Integer +--E 209 + +--S 210 of 578 +d0041:= D(m0041,x) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (197) x %e +--R Type: Expression Integer +--E 210 + +--S 211 of 578 +t0042:= x^2*exp(1)^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (198) x %e +--R Type: Expression Integer +--E 211 + +--S 212 of 578 +r0042:= -1/4*b*exp(1)^(a+b*x+c*x^2)/c^2+1/2*exp(1)^(a+b*x+c*x^2)*x/c+_ + 1/8*(b^2-2*c)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)/c^(1/2))/c^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 578 +a0042:= integrate(t0042,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (199) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 213 + +--S 214 of 578 +m0042:= a0042-r0042 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (200) | %A %e d%A - r0042 +--R ++ +--R Type: Expression Integer +--E 214 + +--S 215 of 578 +d0042:= D(m0042,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (201) x %e +--R Type: Expression Integer +--E 215 + +--S 216 of 578 +t0043:= x^3*exp(1)^((a+b*x)*(c+d*x)) +--R +--R +--R 2 +--R 3 b d x + (a d + b c)x + a c +--R (202) x %e +--R Type: Expression Integer +--E 216 + +--S 217 of 578 +r0043:= -1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^2/d^2+_ + 1/8*(b*c+a*d)^2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^3/d^3-_ + 1/4*(b*c+a*d)*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x/b^2/d^2+_ + 1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x^2/b/d-_ + 1/16*(b^3*c^3-3*b^2*c*(2-a*c)*d-3*a*b*(2-a*c)*d^2+_ + a^3*d^3)*%pi^(1/2)*erfi(1/2*(b*c+a*d+2*b*x*d)/b^(1/2)/d^(1/2))/_ + (exp(1)^(1/4*(b*c-a*d)^2/b/d))/b^(7/2)/d^(7/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 217 + +--S 218 of 578 +a0043:= integrate(t0043,x) +--R +--R +--R x 2 +--R ++ 3 (%A b + %A a)d + (%A b + a)c +--R (203) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 218 + +--S 219 of 578 +m0043:= a0043-r0043 +--R +--R +--R x 2 +--R ++ 3 (%A b + %A a)d + (%A b + a)c +--R (204) | %A %e d%A - r0043 +--R ++ +--R Type: Expression Integer +--E 219 + +--S 220 of 578 +d0043:= D(m0043,x) +--R +--R +--R 2 +--R 3 b d x + (a d + b c)x + a c +--R (205) x %e +--R Type: Expression Integer +--E 220 + +--S 221 of 578 +t0044:= x^2*exp(1)^((a+b*x)*(c+d*x)) +--R +--R +--R 2 +--R 2 b d x + (a d + b c)x + a c +--R (206) x %e +--R Type: Expression Integer +--E 221 + +--S 222 of 578 +r0044:= -1/4*(b*c+a*d)*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^2/d^2+_ + 1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x/b/d+_ + 1/8*(b^2*c^2-2*b*(1-a*c)*d+a^2*d^2)*%pi^(1/2)*_ + erfi(1/2*(b*c+a*d+2*b*x*d)/b^(1/2)/d^(1/2))/_ + (exp(1)^(1/4*(b*c-a*d)^2/b/d))/b^(5/2)/d^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 578 +a0044:= integrate(t0044,x) +--R +--R +--R x 2 +--R ++ 2 (%A b + %A a)d + (%A b + a)c +--R (207) | %A %e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 578 +m0044:= a0044-r0044 +--R +--R +--R x 2 +--R ++ 2 (%A b + %A a)d + (%A b + a)c +--R (208) | %A %e d%A - r0044 +--R ++ +--R Type: Expression Integer +--E 224 + +--S 225 of 578 +d0044:= D(m0044,x) +--R +--R +--R 2 +--R 2 b d x + (a d + b c)x + a c +--R (209) x %e +--R Type: Expression Integer +--E 225 + +--S 226 of 578 +t0045:= x^3*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (210) x f +--R Type: Expression Integer +--E 226 + +--S 227 of 578 +r0045:= -1/2*f^(a+b*x+c*x^2)/c^2/log(f)^2+1/8*b^2*f^(a+b*x+c*x^2)/c^3/log(f)-_ + 1/4*b*f^(a+b*x+c*x^2)*x/c^2/log(f)+1/2*f^(a+b*x+c*x^2)*x^2/c/log(f)+_ + 1/16*b*f^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_ + (6*c-b^2*log(f))/c^(7/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 578 +a0045:= integrate(t0045,x) +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (211) | %A f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 578 +m0045:= a0045-r0045 +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (212) | %A f d%A - r0045 +--R ++ +--R Type: Expression Integer +--E 229 + +--S 230 of 578 +d0045:= D(m0045,x) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (213) x f +--R Type: Expression Integer +--E 230 + +--S 231 of 578 +t0046:= x^2*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (214) x f +--R Type: Expression Integer +--E 231 + +--S 232 of 578 +r0046:= -1/4*b*f^(a+b*x+c*x^2)/c^2/log(f)+1/2*f^(a+b*x+c*x^2)*x/c/log(f)-_ + 1/8*f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_ + log(f)^(1/2)/c^(1/2))*(2*c-b^2*log(f))/c^(5/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 578 +a0046:= integrate(t0046,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (215) | %A f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 578 +m0046:= a0046-r0046 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (216) | %A f d%A - r0046 +--R ++ +--R Type: Expression Integer +--E 234 + +--S 235 of 578 +d0046:= D(m0046,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (217) x f +--R Type: Expression Integer +--E 235 + +--S 236 of 578 +t0047:= (d+e*x)^3*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 3 3 2 2 2 3 c x + b x + a +--R (218) (e x + 3d e x + 3d e x + d )f +--R Type: Expression Integer +--E 236 + +--S 237 of 578 +r0047:= -1/2*e^3*f^(a+b*x+c*x^2)/c^2/log(f)^2+_ + 1/8*e*(2*c*d-b*e)^2*f^(a+b*x+c*x^2)/c^3/log(f)+_ + 1/4*e*(2*c*d-b*e)*f^(a+b*x+c*x^2)*(d+e*x)/c^2/log(f)+_ + 1/2*e*f^(a+b*x+c*x^2)*(d+e*x)^2/c/log(f)-_ + 1/16*(2*c*d-b*e)*f^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_ + (6*c*e^2-(2*c*d-b*e)^2*log(f))/c^(7/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 578 +a0047:= integrate(t0047,x) +--R +--R +--R x 2 +--R ++ 3 3 2 2 2 3 %A c + %A b + a +--R (219) | (%A e + 3%A d e + 3%A d e + d )f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 578 +m0047:= a0047-r0047 +--R +--R +--R x 2 +--R ++ 3 3 2 2 2 3 %A c + %A b + a +--R (220) | (%A e + 3%A d e + 3%A d e + d )f d%A - r0047 +--R ++ +--R Type: Expression Integer +--E 239 + +--S 240 of 578 +d0047:= D(m0047,x) +--R +--R +--R 2 +--R 3 3 2 2 2 3 c x + b x + a +--R (221) (e x + 3d e x + 3d e x + d )f +--R Type: Expression Integer +--E 240 + +--S 241 of 578 +t0048:= (d+e*x)^2*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (222) (e x + 2d e x + d )f +--R Type: Expression Integer +--E 241 + +--S 242 of 578 +r0048:= 1/4*e*(4*c*d-b*e)*f^(a+b*x+c*x^2)/c^2/log(f)+_ + 1/2*e^2*f^(a+b*x+c*x^2)*x/c/log(f)-_ + 1/8*f^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_ + (2*c*e^2-(2*c*d-b*e)^2*log(f))/c^(5/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 578 +a0048:= integrate(t0048,x) +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (223) | (%A e + 2%A d e + d )f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 578 +m0048:= a0048-r0048 +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (224) | (%A e + 2%A d e + d )f d%A - r0048 +--R ++ +--R Type: Expression Integer +--E 244 + +--S 245 of 578 +d0048:= D(m0048,x) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (225) (e x + 2d e x + d )f +--R Type: Expression Integer +--E 245 + +--S 246 of 578 +t0049:= (d+e*x)*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R c x + b x + a +--R (226) (e x + d)f +--R Type: Expression Integer +--E 246 + +--S 247 of 578 +r0049:= 1/2*e*f^(a+b*x+c*x^2)/c/log(f)+1/4*(2*c*d-b*e)*_ + f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_ + log(f)^(1/2)/c^(1/2))/c^(3/2)/log(f)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 578 +a0049:= integrate(t0049,x) +--R +--R +--R x 2 +--R ++ %A c + %A b + a +--R (227) | (%A e + d)f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 248 + +--S 249 of 578 +m0049:= a0049-r0049 +--R +--R +--R x 2 +--R ++ %A c + %A b + a +--R (228) | (%A e + d)f d%A - r0049 +--R ++ +--R Type: Expression Integer +--E 249 + +--S 250 of 578 +d0049:= D(m0049,x) +--R +--R +--R 2 +--R c x + b x + a +--R (229) (e x + d)f +--R Type: Expression Integer +--E 250 + +--S 251 of 578 +t0050:= (b+2*c*x)^2*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (230) (4c x + 4b c x + b )f +--R Type: Expression Integer +--E 251 + +--S 252 of 578 +r0050:= -c^(1/2)*f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_ + log(f)^(1/2)/c^(1/2))/log(f)^(3/2)+f^(a+b*x+c*x^2)*(b+2*c*x)/log(f) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 578 +a0050:= integrate(t0050,x) +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (231) | (4%A c + 4%A b c + b )f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 253 + +--S 254 of 578 +m0050:= a0050-r0050 +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (232) | (4%A c + 4%A b c + b )f d%A - r0050 +--R ++ +--R Type: Expression Integer +--E 254 + +--S 255 of 578 +d0050:= D(m0050,x) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (233) (4c x + 4b c x + b )f +--R Type: Expression Integer +--E 255 + +--S 256 of 578 +t0051:= f^(a+b*x^n)*g^(c+d*x^n) +--R +--R +--R n n +--R b x + a d x + c +--R (234) f g +--R Type: Expression Integer +--E 256 + +--S 257 of 578 +r0051:= -f^a*g^c*x*Gamma(1/n,-x^n*(b*log(f)+d*log(g)))/_ + ((-x^n*(b*log(f)+d*log(g)))^(1/n))/n +--R +--R +--R a c _ 1 n +--R x f g | (-,(- d log(g) - b log(f))x ) +--R n +--R (235) - ------------------------------------- +--R 1 +--R - +--R n n +--R n ((- d log(g) - b log(f))x ) +--R Type: Expression Integer +--E 257 + +--S 258 of 578 +a0051:= integrate(t0051,x) +--R +--R +--R x n n +--R ++ b %A + a d %A + c +--R (236) | f g d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 258 + +--S 259 of 578 +m0051:= a0051-r0051 +--R +--R +--R (237) +--R 1 +--R - x n n +--R n n ++ b %A + a d %A + c +--R n ((- d log(g) - b log(f))x ) | f g d%A +--R ++ +--R + +--R a c _ 1 n +--R x f g | (-,(- d log(g) - b log(f))x ) +--R n +--R / +--R 1 +--R - +--R n n +--R n ((- d log(g) - b log(f))x ) +--R Type: Expression Integer +--E 259 + +--S 260 of 578 +d0051:= D(m0051,x) +--R +--R +--R (238) +--R 1 +--R - +--R a c n n +--R f g ((- d log(g) - b log(f))x ) +--R + +--R - n + 1 +--R ------- +--R a c n - 1 n n +--R (d x log(g) + b x log(f))f g x ((- d log(g) - b log(f))x ) +--R * +--R _ 1 n +--R | (-,(- d log(g) - b log(f))x ) +--R n +--R + +--R 1 2 +--R - n n +--R n n b x + a d x + c +--R n (((- d log(g) - b log(f))x ) ) f g +--R + +--R n +--R a c n - 1 (d log(g) + b log(f))x +--R (d n x log(g) + b n x log(f))f g x %e +--R * +--R - n + 1 1 +--R ------- - +--R n n n n +--R ((- d log(g) - b log(f))x ) ((- d log(g) - b log(f))x ) +--R / +--R 1 2 +--R - +--R n n +--R n (((- d log(g) - b log(f))x ) ) +--R Type: Expression Integer +--E 260 + +--S 261 of 578 +t0052:= exp(1)^(4*x)/(a+b*exp(1)^(2*x))^(2/3) +--R +--R +--R 4x +--R %e +--R (239) -------------- +--R +----------+2 +--R 3| 2x +--R \|b %e + a +--R Type: Expression Integer +--E 261 + +--S 262 of 578 +r0052:= 3/8*(a+b*exp(2*x))^(1/3)*(-3*a+b*exp(2*x))/b^2 +--R +--R +--R +----------+ +--R 2x 3| 2x +--R (3b %e - 9a)\|b %e + a +--R (240) --------------------------- +--R 2 +--R 8b +--R Type: Expression Integer +--E 262 + +--S 263 of 578 +a0052:= integrate(t0052,x) +--R +--R +--R +----------+ +--R 2x 3| 2x +--R (3b %e - 9a)\|b %e + a +--R (241) --------------------------- +--R 2 +--R 8b +--R Type: Union(Expression Integer,...) +--E 263 + +--S 264 of 578 +m0052:= a0052-r0052 +--R +--R +--R (242) 0 +--R Type: Expression Integer +--E 264 + +--S 265 of 578 +d0052:= D(m0052,x) +--R +--R +--R (243) 0 +--R Type: Expression Integer +--E 265 + +--S 266 of 578 +t0053:= f^(a+b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R b x + a +--R f +--R (244) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression Integer +--E 266 + +--S 267 of 578 +r0053:= f^(a-1/2*e)*_ + arctan(d^(1/2)*f^(1/2*e+b*x)/c^(1/2))/b/c^(1/2)/d^(1/2)/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 578 +a0053:= integrate(t0053,x) +--R +--R +--R (245) +--R [ +--R log +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R (d %e (%e ) - c) +--R * +--R +----------------------+ +--R | (e - 2a)log(f) +--R \|- c d %e +--R + +--R (e - 2a)log(f) (b x + a)log(f) +--R 2c d %e %e +--R / +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R / +--R +----------------------+ +--R | (e - 2a)log(f) +--R 2b log(f)\|- c d %e +--R , +--R +--------------------+ +--R (b x + a)log(f) | (e - 2a)log(f) +--R %e \|c d %e +--R atan(----------------------------------------) +--R c +--R ----------------------------------------------] +--R +--------------------+ +--R | (e - 2a)log(f) +--R b log(f)\|c d %e +--R Type: Union(List Expression Integer,...) +--E 268 + +--S 269 of 578 +m0053a:= a0053.1-r0053 +--R +--R +--R (246) +--R log +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R (d %e (%e ) - c) +--R * +--R +----------------------+ +--R | (e - 2a)log(f) +--R \|- c d %e +--R + +--R (e - 2a)log(f) (b x + a)log(f) +--R 2c d %e %e +--R / +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R + +--R +----------------------+ +--R | (e - 2a)log(f) +--R - 2b r0053 log(f)\|- c d %e +--R / +--R +----------------------+ +--R | (e - 2a)log(f) +--R 2b log(f)\|- c d %e +--R Type: Expression Integer +--E 269 + +--S 270 of 578 +d0053a:= D(m0053a,x) +--R +--R +--R (b x + a)log(f) +--R %e +--R (247) ------------------------------------------ +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R Type: Expression Integer +--E 270 + +--S 271 of 578 +m0053b:= a0053.2-r0053 +--R +--R +--R (248) +--R +--------------------+ +--R (b x + a)log(f) | (e - 2a)log(f) +--R %e \|c d %e +--R atan(----------------------------------------) +--R c +--R + +--R +--------------------+ +--R | (e - 2a)log(f) +--R - b r0053 log(f)\|c d %e +--R / +--R +--------------------+ +--R | (e - 2a)log(f) +--R b log(f)\|c d %e +--R Type: Expression Integer +--E 271 + +--S 272 of 578 +d0053b:= D(m0053b,x) +--R +--R +--R (b x + a)log(f) +--R %e +--R (249) ------------------------------------------ +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R Type: Expression Integer +--E 272 + +--S 273 of 578 +t0054:= f^(a+2*b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R 2b x + a +--R f +--R (250) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression Integer +--E 273 + +--S 274 of 578 +r0054:= 1/2*f^(a-e)*log(c+d*f^(e+2*b*x))/b/d/log(f) +--R +--R +--R - e + a 2b x + e +--R f log(d f + c) +--R (251) ---------------------------- +--R 2b d log(f) +--R Type: Expression Integer +--E 274 + +--S 275 of 578 +a0054:= integrate(t0054,x) +--R +--R +--R (- e + a)log(f) (2b x + e)log(f) +--R %e log(d %e + c) +--R (252) ---------------------------------------------- +--R 2b d log(f) +--R Type: Union(Expression Integer,...) +--E 275 + +--S 276 of 578 +m0054:= a0054-r0054 +--R +--R +--R (253) +--R (- e + a)log(f) (2b x + e)log(f) - e + a 2b x + e +--R %e log(d %e + c) - f log(d f + c) +--R ----------------------------------------------------------------------------- +--R 2b d log(f) +--R Type: Expression Integer +--E 276 + +--S 277 of 578 +d0054:= D(m0054,x) +--R +--R +--R (254) +--R 2b x + e (- e + a)log(f) - e + a 2b x + e +--R ((d f + c)%e - d f f ) +--R * +--R (2b x + e)log(f) +--R %e +--R + +--R - e + a 2b x + e +--R - c f f +--R / +--R 2 2b x + e (2b x + e)log(f) 2b x + e 2 +--R (d f + c d)%e + c d f + c +--R Type: Expression Integer +--E 277 + +--S 278 of 578 +t0055:= f^(a+3*b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R 3b x + a +--R f +--R (255) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression Integer +--E 278 + +--S 279 of 578 +r0055:= -(-f^(a-e+b*x)*d^(1/2)+c^(1/2)*f^(a-2*e)*(f^e)^(1/2)*_ + arctan(d^(1/2)*f^(b*x)*(f^e)^(1/2)/c^(1/2)))/b/d^(3/2)/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 279 + +--S 280 of 578 +a0055:= integrate(t0055,x) +--R +--R +--R (256) +--R [ +--R (- 3e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) - 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R 2%e %e +--R / +--R 2b d log(f) +--R , +--R +--R (2b x + e)log(f) +--R (- 3e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R - |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R %e %e +--R / +--R b d log(f) +--R ] +--R Type: Union(List Expression Integer,...) +--E 280 + +--S 281 of 578 +m0055a:= a0055.1-r0055 +--R +--R +--R (257) +--R (- 3e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) - 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R 2%e %e - 2b d r0055 log(f) +--R / +--R 2b d log(f) +--R Type: Expression Integer +--E 281 + +--S 282 of 578 +d0055a:= D(m0055a,x) +--R +--R +--R (- 3e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (258) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression Integer +--E 282 + +--S 283 of 578 +m0055b:= a0055.2-r0055 +--R +--R +--R (259) +--R (2b x + e)log(f) +--R (- 3e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R - |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R %e %e - b d r0055 log(f) +--R / +--R b d log(f) +--R Type: Expression Integer +--E 283 + +--S 284 of 578 +d0055b:= D(m0055b,x) +--R +--R +--R (- 3e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (260) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression Integer +--E 284 + +--S 285 of 578 +t0056:= f^(a+5*b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R 5b x + a +--R f +--R (261) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression Integer +--E 285 + +--S 286 of 578 +r0056:= -1/3/d^(5/2)*(3*c*f^(a-2*e+b*x)*d^(1/2)-f^(a-e+3*b*x)*d^(3/2)-_ + 3*c^(3/2)*f^(a-3*e)*(f^e)^(1/2)*_ + arctan(d^(1/2)*f^(b*x)*(f^e)^(1/2)/c^(1/2)))/b/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 578 +a0056:= integrate(t0056,x) +--R +--R +--R (262) +--R [ +--R (- 5e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R 3c |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) + 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R 2d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R - 6c %e %e +--R / +--R 2 +--R 6b d log(f) +--R , +--R +--R (2b x + e)log(f) +--R (- 5e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R 3c |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R - 3c %e %e +--R / +--R 2 +--R 3b d log(f) +--R ] +--R Type: Union(List Expression Integer,...) +--E 287 + +--S 288 of 578 +m0056a:= a0056.1-r0056 +--R +--R +--R (263) +--R (- 5e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R 3c |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) + 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R 2d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 2 +--R - 6c %e %e - 6b d r0056 log(f) +--R / +--R 2 +--R 6b d log(f) +--R Type: Expression Integer +--E 288 + +--S 289 of 578 +d0056a:= D(m0056a,x) +--R +--R +--R (- 5e + 2a)log(f) (2b x + e)log(f) 5 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (264) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression Integer +--E 289 + +--S 290 of 578 +m0056b:= a0056.2-r0056 +--R +--R +--R (265) +--R (2b x + e)log(f) +--R (- 5e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R 3c |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 2 +--R - 3c %e %e - 3b d r0056 log(f) +--R / +--R 2 +--R 3b d log(f) +--R Type: Expression Integer +--E 290 + +--S 291 of 578 +d0056b:= D(m0056b,x) +--R +--R +--R (- 5e + 2a)log(f) (2b x + e)log(f) 5 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (266) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression Integer +--E 291 + +--S 292 of 578 +t0057:= x*exp(x)/(1+exp(1)^(2*x)) +--R +--R +--R x +--R x %e +--R (267) -------- +--R 2x +--R %e + 1 +--R Type: Expression Integer +--E 292 + +--S 293 of 578 +r0057:= x*arctan(exp(x))-_ + 1/2*%i*polylog(2,-%i*exp(x))+_ + 1/2*%i*polylog(2,%i*exp(x)) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 293 + +--S 294 of 578 +a0057:= integrate(t0057,x) +--R +--R +--R x %A +--R ++ %A %e +--R (268) | --------- d%A +--R ++ 2%A +--R %e + 1 +--R Type: Union(Expression Integer,...) +--E 294 + +--S 295 of 578 +m0057:= a0057-r0057 +--R +--R +--R x %A +--R ++ %A %e +--R (269) | --------- d%A - r0057 +--R ++ 2%A +--R %e + 1 +--R Type: Expression Integer +--E 295 + +--S 296 of 578 +d0057:= D(m0057,x) +--R +--R +--R x +--R x %e +--R (270) -------- +--R 2x +--R %e + 1 +--R Type: Expression Integer +--E 296 + +--S 297 of 578 +t0058:= x^2*exp(x)/(1+exp(1)^(2*x)) +--R +--R +--R 2 x +--R x %e +--R (271) -------- +--R 2x +--R %e + 1 +--R Type: Expression Integer +--E 297 + +--S 298 of 578 +r0058:= x^2*arctan(exp(x))-%i*x*_ + polylog(2,-%i*exp(x))+%i*x*polylog(2,%i*exp(x))+_ + %i*polylog(3,-%i*exp(x))-%i*polylog(3,%i*exp(x)) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 298 + +--S 299 of 578 +a0058:= integrate(t0058,x) +--R +--R +--R x 2 %A +--R ++ %A %e +--R (272) | --------- d%A +--R ++ 2%A +--R %e + 1 +--R Type: Union(Expression Integer,...) +--E 299 + +--S 300 of 578 +m0058:= a0058-r0058 +--R +--R +--R x 2 %A +--R ++ %A %e +--R (273) | --------- d%A - r0058 +--R ++ 2%A +--R %e + 1 +--R Type: Expression Integer +--E 300 + +--S 301 of 578 +d0058:= D(m0058,x) +--R +--R +--R 2 x +--R x %e +--R (274) -------- +--R 2x +--R %e + 1 +--R Type: Expression Integer +--E 301 + +--S 302 of 578 +t0059:= x^3*exp(x)/(1+exp(1)^(2*x)) +--R +--R +--R 3 x +--R x %e +--R (275) -------- +--R 2x +--R %e + 1 +--R Type: Expression Integer +--E 302 + +--S 303 of 578 +r0059:= x^3*arctan(exp(x))-3/2*%i*x^2*polylog(2,-%i*exp(x))+_ + 3/2*%i*x^2*polylog(2,%i*exp(x))+_ + 3*%i*x*polylog(3,-%i*exp(x))-_ + 3*%i*x*polylog(3,%i*exp(x))-_ + 3*%i*polylog(4,-%i*exp(x))+_ + 3*%i*polylog(4,%i*exp(x)) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 303 + +--S 304 of 578 +a0059:= integrate(t0059,x) +--R +--R +--R x 3 %A +--R ++ %A %e +--R (276) | --------- d%A +--R ++ 2%A +--R %e + 1 +--R Type: Union(Expression Integer,...) +--E 304 + +--S 305 of 578 +m0059:= a0059-r0059 +--R +--R +--R x 3 %A +--R ++ %A %e +--R (277) | --------- d%A - r0059 +--R ++ 2%A +--R %e + 1 +--R Type: Expression Integer +--E 305 + +--S 306 of 578 +d0059:= D(m0059,x) +--R +--R +--R 3 x +--R x %e +--R (278) -------- +--R 2x +--R %e + 1 +--R Type: Expression Integer +--E 306 + +--S 307 of 578 +t0060:= x*exp(x)/(1-exp(1)^(2*x)) +--R +--R +--R x +--R x %e +--R (279) - -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 307 + +--S 308 of 578 +r0060:= x*arctanh(exp(x))+1/2*polylog(2,-exp(x))-1/2*polylog(2,exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 308 + +--S 309 of 578 +a0060:= integrate(t0060,x) +--R +--R +--R x %A +--R ++ %A %e +--R (280) | - --------- d%A +--R ++ 2%A +--R %e - 1 +--R Type: Union(Expression Integer,...) +--E 309 + +--S 310 of 578 +m0060:= a0060-r0060 +--R +--R +--R x %A +--R ++ %A %e +--R (281) | - --------- d%A - r0060 +--R ++ 2%A +--R %e - 1 +--R Type: Expression Integer +--E 310 + +--S 311 of 578 +d0060:= D(m0060,x) +--R +--R +--R x +--R x %e +--R (282) - -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 311 + +--S 312 of 578 +t0061:= x^2*exp(x)/(1-exp(1)^(2*x)) +--R +--R +--R 2 x +--R x %e +--R (283) - -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 312 + +--S 313 of 578 +r0061:= x^2*arctanh(exp(x))+x*polylog(2,-exp(x))-_ + x*polylog(2,exp(x))-_ + polylog(3,-exp(x))+polylog(3,exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 313 + +--S 314 of 578 +a0061:= integrate(t0061,x) +--R +--R +--R x 2 %A +--R ++ %A %e +--R (284) | - --------- d%A +--R ++ 2%A +--R %e - 1 +--R Type: Union(Expression Integer,...) +--E 314 + +--S 315 of 578 +m0061:= a0061-r0061 +--R +--R +--R x 2 %A +--R ++ %A %e +--R (285) | - --------- d%A - r0061 +--R ++ 2%A +--R %e - 1 +--R Type: Expression Integer +--E 315 + +--S 316 of 578 +d0061:= D(m0061,x) +--R +--R +--R 2 x +--R x %e +--R (286) - -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 316 + +--S 317 of 578 +t0062:= x^3*exp(x)/(1-exp(1)^(2*x)) +--R +--R +--R 3 x +--R x %e +--R (287) - -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 317 + +--S 318 of 578 +r0062:= x^3*arctanh(exp(x))+3/2*x^2*polylog(2,-exp(x))-_ + 3/2*x^2*polylog(2,exp(x))-3*x*polylog(3,-exp(x))+_ + 3*x*polylog(3,exp(x))+3*polylog(4,-exp(x))-3*polylog(4,exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 318 + +--S 319 of 578 +a0062:= integrate(t0062,x) +--R +--R +--R x 3 %A +--R ++ %A %e +--R (288) | - --------- d%A +--R ++ 2%A +--R %e - 1 +--R Type: Union(Expression Integer,...) +--E 319 + +--S 320 of 578 +m0062:= a0062-r0062 +--R +--R +--R x 3 %A +--R ++ %A %e +--R (289) | - --------- d%A - r0062 +--R ++ 2%A +--R %e - 1 +--R Type: Expression Integer +--E 320 + +--S 321 of 578 +d0062:= D(m0062,x) +--R +--R +--R 3 x +--R x %e +--R (290) - -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 321 + +--S 322 of 578 +t0063:= f^x/(a+b*f^(2*x)) +--R +--R +--R x +--R f +--R (291) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 322 + +--S 323 of 578 +r0063:= arctan(b^(1/2)*f^x/a^(1/2))/a^(1/2)/b^(1/2)/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 323 + +--S 324 of 578 +a0063:= integrate(t0063,x) +--R +--R +--R (292) +--R +-----+ x log(f) 2 x log(f) +-----+ +--R b\|- a b (%e ) + 2a b %e - a\|- a b +--R log(----------------------------------------------------) +--R x log(f) 2 +--R b (%e ) + a +--R [---------------------------------------------------------, +--R +-----+ +--R 2log(f)\|- a b +--R +---+ x log(f) +--R \|a b %e +--R atan(----------------) +--R a +--R ----------------------] +--R +---+ +--R log(f)\|a b +--R Type: Union(List Expression Integer,...) +--E 324 + +--S 325 of 578 +m0063a:= a0063.1-r0063 +--R +--R +--R (293) +--R +-----+ x log(f) 2 x log(f) +-----+ +--R b\|- a b (%e ) + 2a b %e - a\|- a b +--R log(----------------------------------------------------) +--R x log(f) 2 +--R b (%e ) + a +--R + +--R +-----+ +--R - 2r0063 log(f)\|- a b +--R / +--R +-----+ +--R 2log(f)\|- a b +--R Type: Expression Integer +--E 325 + +--S 326 of 578 +d0063a:= D(m0063a,x) +--R +--R +--R x log(f) +--R %e +--R (294) ------------------- +--R x log(f) 2 +--R b (%e ) + a +--R Type: Expression Integer +--E 326 + +--S 327 of 578 +m0063b:= a0063.2-r0063 +--R +--R +--R +---+ x log(f) +--R \|a b %e +---+ +--R atan(----------------) - r0063 log(f)\|a b +--R a +--R (295) ------------------------------------------- +--R +---+ +--R log(f)\|a b +--R Type: Expression Integer +--E 327 + +--S 328 of 578 +d0063b:= D(m0063b,x) +--R +--R +--R x log(f) +--R %e +--R (296) ------------------- +--R x log(f) 2 +--R b (%e ) + a +--R Type: Expression Integer +--E 328 + +--S 329 of 578 +t0064:= x*f^x/(a+b*f^(2*x)) +--R +--R +--R x +--R x f +--R (297) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 329 + +--S 330 of 578 +r0064:= 1/2*(2*x*arctan(b^(1/2)*f^x/a^(1/2))*log(f)-_ + %i*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))+_ + %i*polylog(2,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^2 +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 330 + +--S 331 of 578 +a0064:= integrate(t0064,x) +--R +--R +--R x %A +--R ++ %A f +--R (298) | ---------- d%A +--R ++ 2%A +--R b f + a +--R Type: Union(Expression Integer,...) +--E 331 + +--S 332 of 578 +m0064:= a0064-r0064 +--R +--R +--R x %A +--R ++ %A f +--R (299) | ---------- d%A - r0064 +--R ++ 2%A +--R b f + a +--R Type: Expression Integer +--E 332 + +--S 333 of 578 +d0064:= D(m0064,x) +--R +--R +--R x +--R x f +--R (300) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 333 + +--S 334 of 578 +t0065:= x^2*f^x/(a+b*f^(2*x)) +--R +--R +--R 2 x +--R x f +--R (301) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 334 + +--S 335 of 578 +r0065:= (x^2*arctan(b^(1/2)*f^x/a^(1/2))*log(f)^2-_ + %i*x*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))*log(f)+_ + %i*x*polylog(2,%i*b^(1/2)*f^x/a^(1/2))*log(f)+_ + %i*polylog(3,-%i*b^(1/2)*f^x/a^(1/2))-_ + %i*polylog(3,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^3 +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 335 + +--S 336 of 578 +a0065:= integrate(t0065,x) +--R +--R +--R x 2 %A +--R ++ %A f +--R (302) | ---------- d%A +--R ++ 2%A +--R b f + a +--R Type: Union(Expression Integer,...) +--E 336 + +--S 337 of 578 +m0065:= a0065-r0065 +--R +--R +--R x 2 %A +--R ++ %A f +--R (303) | ---------- d%A - r0065 +--R ++ 2%A +--R b f + a +--R Type: Expression Integer +--E 337 + +--S 338 of 578 +d0065:= D(m0065,x) +--R +--R +--R 2 x +--R x f +--R (304) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 338 + +--S 339 of 578 +t0066:= x^3*f^x/(a+b*f^(2*x)) +--R +--R +--R 3 x +--R x f +--R (305) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 339 + +--S 340 of 578 +r0066:= 1/2*(2*x^3*arctan(b^(1/2)*f^x/a^(1/2))*log(f)^3-_ + 3*%i*x^2*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))*log(f)^2+_ + 3*%i*x^2*polylog(2,%i*b^(1/2)*f^x/a^(1/2))*log(f)^2+_ + 6*%i*x*polylog(3,-%i*b^(1/2)*f^x/a^(1/2))*log(f)-_ + 6*%i*x*polylog(3,%i*b^(1/2)*f^x/a^(1/2))*log(f)-_ + 6*%i*polylog(4,-%i*b^(1/2)*f^x/a^(1/2))+_ + 6*%i*polylog(4,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^4 +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 340 + +--S 341 of 578 +a0066:= integrate(t0066,x) +--R +--R +--R x 3 %A +--R ++ %A f +--R (306) | ---------- d%A +--R ++ 2%A +--R b f + a +--R Type: Union(Expression Integer,...) +--E 341 + +--S 342 of 578 +m0066:= a0066-r0066 +--R +--R +--R x 3 %A +--R ++ %A f +--R (307) | ---------- d%A - r0066 +--R ++ 2%A +--R b f + a +--R Type: Expression Integer +--E 342 + +--S 343 of 578 +d0066:= D(m0066,x) +--R +--R +--R 3 x +--R x f +--R (308) --------- +--R 2x +--R b f + a +--R Type: Expression Integer +--E 343 + +--S 344 of 578 +t0067:= x/(3+3*exp(x)+exp(1)^(2*x)) +--R +--R +--R x +--R (309) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression Integer +--E 344 + +--S 345 of 578 +r0067:= -1/3*%i*x^2*3^(1/2)/(3-%i*3^(1/2))+_ + 1/3*%i*x^2*3^(1/2)/(3+%i*3^(1/2))+_ + 2/3*%i*x*log(1+2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 2/3*%i*x*log(1+2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))+_ + 2/3*%i*polylog(2,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 2/3*%i*polylog(2,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 345 + +--S 346 of 578 +a0067:= integrate(t0067,x) +--R +--R +--R x +--R ++ %A +--R (310) | ----------------- d%A +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Union(Expression Integer,...) +--E 346 + +--S 347 of 578 +m0067:= a0067-r0067 +--R +--R +--R x +--R ++ %A +--R (311) | ----------------- d%A - r0067 +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Expression Integer +--E 347 + +--S 348 of 578 +d0067:= D(m0067,x) +--R +--R +--R x +--R (312) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression Integer +--E 348 + +--S 349 of 578 +t0068:= x/(a+b*exp(x)+c*exp(1)^(2*x)) +--R +--R +--R x +--R (313) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression Integer +--E 349 + +--S 350 of 578 +r0068:= c*x^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + c*x^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x*log(1+2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/_ + (b-(b^2-4*a*c)^(1/2))+2*c*x*log(1+2*c*exp(x)/_ + (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*polylog(2,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+_ + 2*c*polylog(2,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 350 + +--S 351 of 578 +a0068:= integrate(t0068,x) +--R +--R +--R x +--R ++ %A +--R (314) | -------------------- d%A +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Union(Expression Integer,...) +--E 351 + +--S 352 of 578 +m0068:= a0068-r0068 +--R +--R +--R x +--R ++ %A +--R (315) | -------------------- d%A - r0068 +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Expression Integer +--E 352 + +--S 353 of 578 +d0068:= D(m0068,x) +--R +--R +--R x +--R (316) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression Integer +--E 353 + +--S 354 of 578 +t0069:= x^2/(-1+exp(x)+exp(1)^(2*x)) +--R +--R +--R 2 +--R x +--R (317) -------------- +--R 2x x +--R %e + %e - 1 +--R Type: Expression Integer +--E 354 + +--S 355 of 578 +r0069:= 2/15*x^3*5^(1/2)/(1-5^(1/2))-2/15*x^3*5^(1/2)/(5^(1/2)+1)-_ + 2/5*x^2*log(1+2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))+_ + 2/5*x^2*log(1+2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)-_ + 4/5*x*polylog(2,-2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))+_ + 4/5*x*polylog(2,-2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)+_ + 4/5*polylog(3,-2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))-_ + 4/5*polylog(3,-2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 355 + +--S 356 of 578 +a0069:= integrate(t0069,x) +--R +--R +--R x 2 +--R ++ %A +--R (318) | ---------------- d%A +--R ++ 2%A %A +--R %e + %e - 1 +--R Type: Union(Expression Integer,...) +--E 356 + +--S 357 of 578 +m0069:= a0069-r0069 +--R +--R +--R x 2 +--R ++ %A +--R (319) | ---------------- d%A - r0069 +--R ++ 2%A %A +--R %e + %e - 1 +--R Type: Expression Integer +--E 357 + +--S 358 of 578 +d0069:= D(m0069,x) +--R +--R +--R 2 +--R x +--R (320) -------------- +--R 2x x +--R %e + %e - 1 +--R Type: Expression Integer +--E 358 + +--S 359 of 578 +t0070:= x^2/(3+3*exp(x)+exp(1)^(2*x)) +--R +--R +--R 2 +--R x +--R (321) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression Integer +--E 359 + +--S 360 of 578 +r0070:= -2/9*%i*x^3*3^(1/2)/(3-%i*3^(1/2))+2/9*%i*x^3*3^(1/2)/(3+%i*3^(1/2))+_ + 2/3*%i*x^2*log(1+2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 2/3*%i*x^2*log(1+2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))+_ + 4/3*%i*x*polylog(2,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 4/3*%i*x*polylog(2,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))-_ + 4/3*%i*polylog(3,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))+_ + 4/3*%i*polylog(3,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 360 + +--S 361 of 578 +a0070:= integrate(t0070,x) +--R +--R +--R x 2 +--R ++ %A +--R (322) | ----------------- d%A +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Union(Expression Integer,...) +--E 361 + +--S 362 of 578 +m0070:= a0070-r0070 +--R +--R +--R x 2 +--R ++ %A +--R (323) | ----------------- d%A - r0070 +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Expression Integer +--E 362 + +--S 363 of 578 +d0070:= D(m0070,x) +--R +--R +--R 2 +--R x +--R (324) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression Integer +--E 363 + +--S 364 of 578 +t0071:= x^2/(a+b*exp(x)+c*exp(1)^(2*x)) +--R +--R +--R 2 +--R x +--R (325) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression Integer +--E 364 + +--S 365 of 578 +r0071:= 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x^2*log(1+2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+2*c*x^2*log(1+2*c*exp(x)/_ + (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 4*c*x*polylog(2,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+_ + 4*c*x*polylog(2,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))+_ + 4*c*polylog(3,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + 4*c*polylog(3,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 365 + +--S 366 of 578 +a0071:= integrate(t0071,x) +--R +--R +--R x 2 +--R ++ %A +--R (326) | -------------------- d%A +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Union(Expression Integer,...) +--E 366 + +--S 367 of 578 +m0071:= a0071-r0071 +--R +--R +--R x 2 +--R ++ %A +--R (327) | -------------------- d%A - r0071 +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Expression Integer +--E 367 + +--S 368 of 578 +d0071:= D(m0071,x) +--R +--R +--R 2 +--R x +--R (328) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression Integer +--E 368 + +--S 369 of 578 +t0072:= 1/(1+2*f^(c+d*x)+f^(2*c+2*d*x)) +--R +--R +--R 1 +--R (329) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 369 + +--S 370 of 578 +r0072:= x+1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f) +--R +--R +--R (330) +--R d x + c d x + c d x + c +--R (- f - 1)log(f + 1) + d x log(f)f + d x log(f) + 1 +--R ----------------------------------------------------------------------- +--R d x + c +--R d log(f)f + d log(f) +--R Type: Expression Integer +--E 370 + +--S 371 of 578 +a0072:= integrate(t0072,x) +--R +--R +--R (331) +--R (d x + c)log(f) (d x + c)log(f) +--R (- %e - 1)log(%e + 1) +--R + +--R (d x + c)log(f) +--R d x log(f)%e + d x log(f) + 1 +--R / +--R (d x + c)log(f) +--R d log(f)%e + d log(f) +--R Type: Union(Expression Integer,...) +--E 371 + +--S 372 of 578 +m0072:= a0072-r0072 +--R +--R +--R (332) +--R d x + c (d x + c)log(f) d x + c +--R ((- f - 1)%e - f - 1) +--R * +--R (d x + c)log(f) +--R log(%e + 1) +--R + +--R d x + c (d x + c)log(f) d x + c d x + c +--R ((f + 1)%e + f + 1)log(f + 1) +--R + +--R (d x + c)log(f) d x + c +--R - %e + f +--R / +--R d x + c (d x + c)log(f) d x + c +--R (d log(f)f + d log(f))%e + d log(f)f +--R + +--R d log(f) +--R Type: Expression Integer +--E 372 + +--S 373 of 578 +d0072:= D(m0072,x) +--R +--R +--R (333) +--R (d x + c)log(f) 2 (d x + c)log(f) d x + c 2 d x + c +--R - (%e ) - 2%e + (f ) + 2f +--R / +--R d x + c 2 d x + c (d x + c)log(f) 2 +--R ((f ) + 2f + 1)(%e ) +--R + +--R d x + c 2 d x + c (d x + c)log(f) d x + c 2 d x + c +--R (2(f ) + 4f + 2)%e + (f ) + 2f +--R + +--R 1 +--R Type: Expression Integer +--E 373 + +--S 374 of 578 +t0073:= 1/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)) +--R +--R +--R 1 +--R (334) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression Integer +--E 374 + +--S 375 of 578 +r0073:= x/a+b*arctanh((b+2*c*f^(c+d*x))/(b^2-4*a*c)^(1/2))/a/_ + (b^2-4*a*c)^(1/2)/d/log(f)-1/2*log(a+b*f^(c+d*x)+_ + c*f^(2*c+2*d*x))/a/d/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 375 + +--S 376 of 578 +a0073:= integrate(t0073,x) +--R +--R +--R (335) +--R [ +--R +-----------+ +--R | 2 (d x + c)log(f) 2 (d x + c)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (d x + c)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (d x + c)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2d x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a d log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (d x + c)log(f) 2 (d x + c)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (d x + c)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2d x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a d log(f)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 376 + +--S 377 of 578 +m0073:= a0073-r0073 +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R List Expression Integer +--R Variable r0073 +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 578 +d0073:= D(m0073,x) +--R +--R +--R (336) 0 +--R Type: Polynomial Integer +--E 378 + +--S 379 of 578 +t0074:= x/(1+2*f^(c+d*x)+f^(2*c+2*d*x)) +--R +--R +--R x +--R (337) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 379 + +--S 380 of 578 +r0074:= 1/2*x^2-x/d/log(f)+log(1+f^(c+d*x))/d^2/log(f)^2+_ + x*(1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f))-_ + polylog(2,-f^(c+d*x))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 380 + +--S 381 of 578 +a0074:= integrate(t0074,x) +--R +--R +--R x +--R ++ %A +--R (338) | ---------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Union(Expression Integer,...) +--E 381 + +--S 382 of 578 +m0074:= a0074-r0074 +--R +--R +--R x +--R ++ %A +--R (339) | ---------------------------- d%A - r0074 +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 382 + +--S 383 of 578 +d0074:= D(m0074,x) +--R +--R +--R x +--R (340) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 383 + +--S 384 of 578 +t0075:= x/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)) +--R +--R +--R x +--R (341) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression Integer +--E 384 + +--S 385 of 578 +r0075:= c*x^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + c*x^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x*log(1+2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d/log(f)+_ + 2*c*x*log(1+2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d/log(f)-_ + 2*c*polylog(2,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_ + 2*c*polylog(2,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 385 + +--S 386 of 578 +a0075:= integrate(t0075,x) +--R +--R +--R x +--R ++ %A +--R (342) | ------------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Union(Expression Integer,...) +--E 386 + +--S 387 of 578 +m0075:= a0075-r0075 +--R +--R +--R x +--R ++ %A +--R (343) | ------------------------------- d%A - r0075 +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Expression Integer +--E 387 + +--S 388 of 578 +d0075:= D(m0075,x) +--R +--R +--R x +--R (344) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression Integer +--E 388 + +--S 389 of 578 +t0076:= x^2/(1+2*f^(c+d*x)+f^(2*c+2*d*x)) +--R +--R +--R 2 +--R x +--R (345) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 389 + +--S 390 of 578 +r0076:= 1/3*x^3-x^2/d/log(f)+2*x*log(1+f^(c+d*x))/d^2/log(f)^2+_ + x^2*(1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f))+_ + 2*(1-d*x*log(f))*polylog(2,-f^(c+d*x))/d^3/log(f)^3+_ + 2*polylog(3,-f^(c+d*x))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 390 + +--S 391 of 578 +a0076:= integrate(t0076,x) +--R +--R +--R x 2 +--R ++ %A +--R (346) | ---------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Union(Expression Integer,...) +--E 391 + +--S 392 of 578 +m0076:= a0076-r0076 +--R +--R +--R x 2 +--R ++ %A +--R (347) | ---------------------------- d%A - r0076 +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 392 + +--S 393 of 578 +d0076:= D(m0076,x) +--R +--R +--R 2 +--R x +--R (348) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression Integer +--E 393 + +--S 394 of 578 +t0077:= x^2/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)) +--R +--R +--R 2 +--R x +--R (349) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression Integer +--E 394 + +--S 395 of 578 +r0077:= 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x^2*log(1+2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d/log(f)+_ + 2*c*x^2*log(1+2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d/log(f)-_ + 4*c*x*polylog(2,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_ + 4*c*x*polylog(2,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_ + 4*c*polylog(3,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^3/log(f)^3-_ + 4*c*polylog(3,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 395 + +--S 396 of 578 +a0077:= integrate(t0077,x) +--R +--R +--R x 2 +--R ++ %A +--R (350) | ------------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Union(Expression Integer,...) +--E 396 + +--S 397 of 578 +m0077:= a0077-r0077 +--R +--R +--R x 2 +--R ++ %A +--R (351) | ------------------------------- d%A - r0077 +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Expression Integer +--E 397 + +--S 398 of 578 +d0077:= D(m0077,x) +--R +--R +--R 2 +--R x +--R (352) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression Integer +--E 398 + +--S 399 of 578 +t0078:= 1/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R 1 +--R (353) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression Integer +--E 399 + +--S 400 of 578 +r0078:= x/a+b*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/a/_ + (b^2-4*a*c)^(1/2)/h/log(f)-1/2*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 400 + +--S 401 of 578 +a0078:= integrate(t0078,x) +--R +--R +--R (354) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 401 + +--S 402 of 578 +m0078a:= a0078.1-r0078 +--R +--R +--R (355) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2h x - 2a h r0078)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression Integer +--E 402 + +--S 403 of 578 +d0078a:= D(m0078a,x) +--R +--R +--R 1 +--R (356) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 403 + +--S 404 of 578 +m0078b:= a0078.2-r0078 +--R +--R +--R (357) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2h x - 2a h r0078)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression Integer +--E 404 + +--S 405 of 578 +d0078b:= D(m0078b,x) +--R +--R +--R 1 +--R (358) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 405 + +--S 406 of 578 +t0079:= 1/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R 1 +--R (359) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression Integer +--E 406 + +--S 407 of 578 +r0079:= x/a+b*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/a/_ + (b^2-4*a*c)^(1/2)/h/log(f)-1/2*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 407 + +--S 408 of 578 +a0079:= integrate(t0079,x) +--R +--R +--R (360) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 408 + +--S 409 of 578 +m0079a:= a0079.1-r0079 +--R +--R +--R (361) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2h x - 2a h r0079)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression Integer +--E 409 + +--S 410 of 578 +d0079a:= D(m0079a,x) +--R +--R +--R 1 +--R (362) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 410 + +--S 411 of 578 +m0079b:= a0079.2-r0079 +--R +--R +--R (363) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2h x - 2a h r0079)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression Integer +--E 411 + +--S 412 of 578 +d0079b:= D(m0079b,x) +--R +--R +--R 1 +--R (364) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 412 + +--S 413 of 578 +t0080:= (d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R h x + g +--R e f + d +--R (365) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression Integer +--E 413 + +--S 414 of 578 +r0080:= d*x/a+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/_ + a/(b^2-4*a*c)^(1/2)/h/log(f)-1/2*d*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 414 + +--S 415 of 578 +a0080:= integrate(t0080,x) +--R +--R +--R (366) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2d h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2d h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 415 + +--S 416 of 578 +m0080a:= a0080.1-r0080 +--R +--R +--R (367) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2d h x - 2a h r0080)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression Integer +--E 416 + +--S 417 of 578 +d0080a:= D(m0080a,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (368) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 417 + +--S 418 of 578 +m0080b:= a0080.2-r0080 +--R +--R +--R (369) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2d h x - 2a h r0080)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression Integer +--E 418 + +--S 419 of 578 +d0080b:= D(m0080b,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (370) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 419 + +--S 420 of 578 +t0081:= (d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R h x + g +--R e f + d +--R (371) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression Integer +--E 420 + +--S 421 of 578 +r0081:= d*x/a+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/_ + a/(b^2-4*a*c)^(1/2)/h/log(f)-1/2*d*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 578 +a0081:= integrate(t0081,x) +--R +--R +--R (372) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2d h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2d h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 422 + +--S 423 of 578 +m0081a:= a0081.1-r0081 +--R +--R +--R (373) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2d h x - 2a h r0081)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression Integer +--E 423 + +--S 424 of 578 +d0081a:= D(m0081a,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (374) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 424 + +--S 425 of 578 +m0081b:= a0081.2-r0081 +--R +--R +--R (375) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2d h x - 2a h r0081)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression Integer +--E 425 + +--S 426 of 578 +d0081b:= D(m0081b,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (376) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression Integer +--E 426 + +--S 427 of 578 +t0082:= x^2/(2+f^(-c-d*x)+f^(c+d*x)) +--R +--R +--R 2 +--R x +--R (377) ------------------------- +--R d x + c - d x - c +--R f + f + 2 +--R Type: Expression Integer +--E 427 + +--S 428 of 578 +r0082:= x^2/d/log(f)-x^2/d/(1+f^(c+d*x))/log(f)-_ + 2*x*log(1+f^(c+d*x))/d^2/log(f)^2-_ + 2*polylog(2,-f^(c+d*x))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 428 + +--S 429 of 578 +a0082:= integrate(t0082,x) +--R +--R +--R x 2 +--R ++ %A +--R (378) | --------------------------- d%A +--R ++ %A d + c - %A d - c +--R f + f + 2 +--R Type: Union(Expression Integer,...) +--E 429 + +--S 430 of 578 +m0082:= a0082-r0082 +--R +--R +--R x 2 +--R ++ %A +--R (379) | --------------------------- d%A - r0082 +--R ++ %A d + c - %A d - c +--R f + f + 2 +--R Type: Expression Integer +--E 430 + +--S 431 of 578 +d0082:= D(m0082,x) +--R +--R +--R 2 +--R x +--R (380) ------------------------- +--R d x + c - d x - c +--R f + f + 2 +--R Type: Expression Integer +--E 431 + +--S 432 of 578 +t0083:= 1/(1-exp(1)^(-x)+2*exp(x)) +--R +--R +--R 1 +--R (381) ---------------- +--R x - x +--R 2%e - %e + 1 +--R Type: Expression Integer +--E 432 + +--S 433 of 578 +r0083:= -2/3*arctanh(1/3+4/3*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 433 + +--S 434 of 578 +a0083:= integrate(t0083,x) +--R +--R +--R x x +--R log(2%e - 1) - log(%e + 1) +--R (382) ---------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 434 + +--S 435 of 578 +m0083:= a0083-r0083 +--R +--R +--R x x +--R log(2%e - 1) - log(%e + 1) - 3r0083 +--R (383) ------------------------------------- +--R 3 +--R Type: Expression Integer +--E 435 + +--S 436 of 578 +d0083:= D(m0083,x) +--R +--R +--R x +--R %e +--R (384) ----------------- +--R x 2 x +--R 2(%e ) + %e - 1 +--R Type: Expression Integer +--E 436 + +--S 437 of 578 +t0084:= x^2/(a+b*exp(1)^(-x)+c*exp(x)) +--R +--R +--R 2 +--R x +--R (385) ------------------- +--R x - x +--R c %e + b %e + a +--R Type: Expression Integer +--E 437 + +--S 438 of 578 +r0084:= (x^2*log(-(a-(a^2-4*b*c)^(1/2)+2*c*exp(x))/(-a+(a^2-4*b*c)^(1/2)))-_ + x^2*log((a+(a^2-4*b*c)^(1/2)+2*c*exp(x))/(a+(a^2-4*b*c)^(1/2)))+_ + 2*x*polylog(2,2*c*exp(x)/(-a+(a^2-4*b*c)^(1/2)))-_ + 2*x*polylog(2,-2*c*exp(x)/(a+(a^2-4*b*c)^(1/2)))-_ + 2*polylog(3,2*c*exp(x)/(-a+(a^2-4*b*c)^(1/2)))+_ + 2*polylog(3,-2*c*exp(x)/(a+(a^2-4*b*c)^(1/2))))/(a^2-4*b*c)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 438 + +--S 439 of 578 +a0084:= integrate(t0084,x) +--R +--R +--R x 2 +--R ++ %A +--R (386) | --------------------- d%A +--R ++ %A - %A +--R c %e + b %e + a +--R Type: Union(Expression Integer,...) +--E 439 + +--S 440 of 578 +m0084:= a0084-r0084 +--R +--R +--R x 2 +--R ++ %A +--R (387) | --------------------- d%A - r0084 +--R ++ %A - %A +--R c %e + b %e + a +--R Type: Expression Integer +--E 440 + +--S 441 of 578 +d0084:= D(m0084,x) +--R +--R +--R 2 +--R x +--R (388) ------------------- +--R x - x +--R c %e + b %e + a +--R Type: Expression Integer +--E 441 + +--S 442 of 578 +t0085:= 1/(a+b*f^(-c-d*x)+c*f^(c+d*x)) +--R +--R +--R 1 +--R (389) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression Integer +--E 442 + +--S 443 of 578 +r0085:= -2*arctanh((a+2*c*f^(c+d*x))/(a^2-4*b*c)^(1/2))/_ + (a^2-4*b*c)^(1/2)/d/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 443 + +--S 444 of 578 +a0085:= integrate(t0085,x) +--R +--R +--R (390) +--R [ +--R log +--R +-----------+ +--R 2 | 2 (d x + c)log(f) 2 +--R 2c \|- 4b c + a (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (d x + c)log(f) +--R (2a c\|- 4b c + a + 8b c - 2a c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2b c + a )\|- 4b c + a + 4a b c - a +--R / +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R / +--R +-----------+ +--R | 2 +--R d log(f)\|- 4b c + a +--R , +--R +---------+ +---------+ +--R | 2 (d x + c)log(f) | 2 +--R 2c\|4b c - a %e + a\|4b c - a +--R 2atan(-----------------------------------------------) +--R 2 +--R 4b c - a +--R ------------------------------------------------------] +--R +---------+ +--R | 2 +--R d log(f)\|4b c - a +--R Type: Union(List Expression Integer,...) +--E 444 + +--S 445 of 578 +m0085a:= a0085.1-r0085 +--R +--R +--R (391) +--R log +--R +-----------+ +--R 2 | 2 (d x + c)log(f) 2 +--R 2c \|- 4b c + a (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (d x + c)log(f) +--R (2a c\|- 4b c + a + 8b c - 2a c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2b c + a )\|- 4b c + a + 4a b c - a +--R / +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R + +--R +-----------+ +--R | 2 +--R - d r0085 log(f)\|- 4b c + a +--R / +--R +-----------+ +--R | 2 +--R d log(f)\|- 4b c + a +--R Type: Expression Integer +--E 445 + +--S 446 of 578 +d0085a:= D(m0085a,x) +--R +--R +--R (d x + c)log(f) +--R %e +--R (392) ------------------------------------------------ +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R Type: Expression Integer +--E 446 + +--S 447 of 578 +m0085b:= a0085.2-r0085 +--R +--R +--R (393) +--R +---------+ +---------+ +--R | 2 (d x + c)log(f) | 2 +--R 2c\|4b c - a %e + a\|4b c - a +--R 2atan(-----------------------------------------------) +--R 2 +--R 4b c - a +--R + +--R +---------+ +--R | 2 +--R - d r0085 log(f)\|4b c - a +--R / +--R +---------+ +--R | 2 +--R d log(f)\|4b c - a +--R Type: Expression Integer +--E 447 + +--S 448 of 578 +d0085b:= D(m0085b,x) +--R +--R +--R (d x + c)log(f) +--R %e +--R (394) ------------------------------------------------ +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R Type: Expression Integer +--E 448 + +--S 449 of 578 +t0086:= x/(a+b*f^(-c-d*x)+c*f^(c+d*x)) +--R +--R +--R x +--R (395) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression Integer +--E 449 + +--S 450 of 578 +r0086:= (x*log(-(a-(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_ + (-a+(a^2-4*b*c)^(1/2)))*d*log(f)-x*log((a+(a^2-4*b*c)^(1/2)+_ + 2*c*f^(c+d*x))/(a+(a^2-4*b*c)^(1/2)))*d*log(f)+_ + polylog(2,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))-_ + polylog(2,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2))))/_ + (a^2-4*b*c)^(1/2)/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 450 + +--S 451 of 578 +a0086:= integrate(t0086,x) +--R +--R +--R x +--R ++ %A +--R (396) | ------------------------------- d%A +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Union(Expression Integer,...) +--E 451 + +--S 452 of 578 +m0086:= a0086-r0086 +--R +--R +--R x +--R ++ %A +--R (397) | ------------------------------- d%A - r0086 +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Expression Integer +--E 452 + +--S 453 of 578 +d0086:= D(m0086,x) +--R +--R +--R x +--R (398) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression Integer +--E 453 + +--S 454 of 578 +t0087:= x^2/(a+b*f^(-c-d*x)+c*f^(c+d*x)) +--R +--R +--R 2 +--R x +--R (399) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression Integer +--E 454 + +--S 455 of 578 +r0087:= (x^2*log(-(a-(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_ + (-a+(a^2-4*b*c)^(1/2)))*d^2*log(f)^2-_ + x^2*log((a+(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_ + (a+(a^2-4*b*c)^(1/2)))*d^2*log(f)^2+_ + 2*x*polylog(2,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))*d*log(f)-_ + 2*x*polylog(2,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2)))*d*log(f)-_ + 2*polylog(3,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))+_ + 2*polylog(3,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2))))/_ + (a^2-4*b*c)^(1/2)/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 455 + +--S 456 of 578 +a0087:= integrate(t0087,x) +--R +--R +--R x 2 +--R ++ %A +--R (400) | ------------------------------- d%A +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Union(Expression Integer,...) +--E 456 + +--S 457 of 578 +m0087:= a0087-r0087 +--R +--R +--R x 2 +--R ++ %A +--R (401) | ------------------------------- d%A - r0087 +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Expression Integer +--E 457 + +--S 458 of 578 +d0087:= D(m0087,x) +--R +--R +--R 2 +--R x +--R (402) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression Integer +--E 458 + +--S 459 of 578 +t0088:= f^(a+b*x+c*x^2)*g^(d+e*x+f*x^2) +--R +--R +--R 2 2 +--R c x + b x + a f x + e x + d +--R (403) f g +--R Type: Expression Integer +--E 459 + +--S 460 of 578 +r0088:= 1/2*f^a*g^d*%pi^(1/2)*erfi(1/2*(b*log(f)+e*log(g)+_ + 2*x*c*log(f)+2*x*f*log(g))/(c*log(f)+f*log(g))^(1/2))/(c*log(f)+_ + f*log(g))^(1/2)*exp(-1/4*(b*log(f)+e*log(g))^2/(c*log(f)+f*log(g))) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 460 + +--S 461 of 578 +a0088:= integrate(t0088,x) +--R +--R +--R x 2 2 +--R ++ %A c + %A b + a %A f + %A e + d +--R (404) | f g d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 461 + +--S 462 of 578 +m0088:= a0088-r0088 +--R +--R +--R x 2 2 +--R ++ %A c + %A b + a %A f + %A e + d +--R (405) | f g d%A - r0088 +--R ++ +--R Type: Expression Integer +--E 462 + +--S 463 of 578 +d0088:= D(m0088,x) +--R +--R +--R 2 2 +--R c x + b x + a f x + e x + d +--R (406) f g +--R Type: Expression Integer +--E 463 + +--S 464 of 578 +t0089:= exp(x)*sin(a+b*x+c*x^2) +--R +--R +--R x 2 +--R (407) %e sin(c x + b x + a) +--R Type: Expression Integer +--E 464 + +--S 465 of 578 +r0089:= 1/4*(-1)^(3/4)*exp(1)^(%i*a+1/4*%i*(1+%i*b)^2/c)*%pi^(1/2)*_ + erf(1/2*(-1)^(1/4)*(1+%i*b+2*%i*c*x)/c^(1/2))/c^(1/2)+_ + 1/4*(-1)^(3/4)*exp(1)^(-%i*a-1/4*%i*(1-%i*b)^2/c)*%pi^(1/2)*_ + erfi(1/2*(-1)^(1/4)*(1-%i*b-2*%i*c*x)/c^(1/2))/c^(1/2) +--R +--R There are 35 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R AlgebraicNumber +--R Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 465 + +--S 466 of 578 +a0089:= integrate(t0089,x) +--R +--R +--R x +--R ++ %A 2 +--R (408) | %e sin(%A c + %A b + a)d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 466 + +--S 467 of 578 +m0089:= a0089-r0089 +--R +--R +--R x +--R ++ %A 2 +--R (409) | %e sin(%A c + %A b + a)d%A - r0089 +--R ++ +--R Type: Expression Integer +--E 467 + +--S 468 of 578 +d0089:= D(m0089,x) +--R +--R +--R x 2 +--R (410) %e sin(c x + b x + a) +--R Type: Expression Integer +--E 468 + +--S 469 of 578 +t0090:= exp(x)*cos(a+b*x+c*x^2) +--R +--R +--R 2 x +--R (411) cos(c x + b x + a)%e +--R Type: Expression Integer +--E 469 + +--S 470 of 578 +r0090:= (-1/8-1/8*%i)*2^(1/2)*%pi^(1/2)*(exp(1/4*%i*(4*a*c+1+2*%i*b-b^2)/c)*_ + erf((1/4+1/4*%i)*2^(1/2)*(1+%i*b+2*%i*c*x)/c^(1/2))+_ + %i*exp(1/4*%i*(-4*a*c-1+2*%i*b+b^2)/c)*_ + erf(1/4*2^(1/2)*(%i*b+2*%i*c*x-1+%i+b+2*c*x)/c^(1/2)))/c^(1/2) +--R +--R There are 35 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R AlgebraicNumber +--R Polynomial Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 470 + +--S 471 of 578 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ 2 %A +--R (412) | cos(%A c + %A b + a)%e d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 471 + +--S 472 of 578 +m0090:= a0090-r0090 +--R +--R +--R x +--R ++ 2 %A +--R (413) | cos(%A c + %A b + a)%e d%A - r0090 +--R ++ +--R Type: Expression Integer +--E 472 + +--S 473 of 578 +d0090:= D(m0090,x) +--R +--R +--R 2 x +--R (414) cos(c x + b x + a)%e +--R Type: Expression Integer +--E 473 + +--S 474 of 578 +t0091:= f^(a+b*x+c*x^2)*sin(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (415) sin(e x + d x + c)f +--R Type: Expression Integer +--E 474 + +--S 475 of 578 +r0091:= 1/4*%i*exp(1)^(-%i*c+(%i*d-b*log(f))^2/(4*%i*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(%i*d-b*log(f)+2*x*(%i*e-c*log(f)))/_ + (%i*e-c*log(f))^(1/2))/(%i*e-c*log(f))^(1/2)-_ + 1/4*%i*exp(1)^(%i*c-(%i*d+b*log(f))^2/(4*%i*e+4*c*log(f)))*f^a*_ + %pi^(1/2)*erfi(1/2*(%i*d+b*log(f)+2*x*(%i*e+c*log(f)))/_ + (%i*e+c*log(f))^(1/2))/(%i*e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 475 + +--S 476 of 578 +a0091:= integrate(t0091,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (416) | sin(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 476 + +--S 477 of 578 +m0091:= a0091-r0091 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (417) | sin(%A e + %A d + c)f d%A - r0091 +--R ++ +--R Type: Expression Integer +--E 477 + +--S 478 of 578 +d0091:= D(m0091,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (418) sin(e x + d x + c)f +--R Type: Expression Integer +--E 478 + +--S 479 of 578 +t0092:= f^(a+b*x+c*x^2)*cos(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (419) cos(e x + d x + c)f +--R Type: Expression Integer +--E 479 + +--S 480 of 578 +r0092:= 1/4*exp(1)^(-%i*c+(%i*d-b*log(f))^2/(4*%i*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(%i*d-b*log(f)+2*x*(%i*e-c*log(f)))/_ + (%i*e-c*log(f))^(1/2))/(%i*e-c*log(f))^(1/2)+_ + 1/4*exp(1)^(%i*c-(%i*d+b*log(f))^2/(4*%i*e+4*c*log(f)))*f^a*_ + %pi^(1/2)*erfi(1/2*(%i*d+b*log(f)+2*x*(%i*e+c*log(f)))/_ + (%i*e+c*log(f))^(1/2))/(%i*e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 480 + +--S 481 of 578 +a0092:= integrate(t0092,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (420) | cos(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 481 + +--S 482 of 578 +m0092:= a0092-r0092 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (421) | cos(%A e + %A d + c)f d%A - r0092 +--R ++ +--R Type: Expression Integer +--E 482 + +--S 483 of 578 +d0092:= D(m0092,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (422) cos(e x + d x + c)f +--R Type: Expression Integer +--E 483 + +--S 484 of 578 +t0093:= exp(1)^(2*x)*cos(exp(x)) +--R +--R +--R 2x x +--R (423) %e cos(%e ) +--R Type: Expression Integer +--E 484 + +--S 485 of 578 +r0093:= cos(exp(x))+exp(x)*sin(exp(x)) +--R +--R +--R x x x +--R (424) %e sin(%e ) + cos(%e ) +--R Type: Expression Integer +--E 485 + +--S 486 of 578 +a0093:= integrate(t0093,x) +--R +--R +--R x x x +--R (425) %e sin(%e ) + cos(%e ) +--R Type: Union(Expression Integer,...) +--E 486 + +--S 487 of 578 +m0093:= a0093-r0093 +--R +--R +--R (426) 0 +--R Type: Expression Integer +--E 487 + +--S 488 of 578 +d0093:= D(m0093,x) +--R +--R +--R (427) 0 +--R Type: Expression Integer +--E 488 + +--S 489 of 578 +t0094:= exp(x)*sec(exp(x)) +--R +--R +--R x x +--R (428) %e sec(%e ) +--R Type: Expression Integer +--E 489 + +--S 490 of 578 +r0094:= arctanh(sin(exp(x))) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 490 + +--S 491 of 578 +a0094:= integrate(t0094,x) +--R +--R +--R x x +--R log(sin(%e ) + 1) - log(sin(%e ) - 1) +--R (429) ------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 491 + +--S 492 of 578 +m0094:= a0094-r0094 +--R +--R +--R x x +--R log(sin(%e ) + 1) - log(sin(%e ) - 1) - 2r0094 +--R (430) ---------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 492 + +--S 493 of 578 +d0094:= D(m0094,x) +--R +--R +--R x x +--R %e cos(%e ) +--R (431) - ------------- +--R x 2 +--R sin(%e ) - 1 +--R Type: Expression Integer +--E 493 + +--S 494 of 578 +t0095:= (cos(x)+sin(x))/(exp(1)^(-x)+sin(x)) +--R +--R +--R sin(x) + cos(x) +--R (432) --------------- +--R - x +--R sin(x) + %e +--R Type: Expression Integer +--E 494 + +--S 495 of 578 +r0095:= log(1+exp(x)*sin(x)) +--R +--R +--R x +--R (433) log(%e sin(x) + 1) +--R Type: Expression Integer +--E 495 + +--S 496 of 578 +a0095:= integrate(t0095,x) +--R +--R +--R - x - x 2 2 +--R log(2%e sin(x) + (%e ) - cos(x) + 1) + 2x +--R (434) ----------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 496 + +--S 497 of 578 +m0095:= a0095-r0095 +--R +--R +--R (435) +--R x - x - x 2 2 +--R - 2log(%e sin(x) + 1) + log(2%e sin(x) + (%e ) - cos(x) + 1) + 2x +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 497 + +--S 498 of 578 +d0095:= D(m0095,x) +--R +--R +--R (436) +--R - x x 2 +--R (- %e + cos(x))%e sin(x) +--R + +--R - x 2 - x x - x +--R ((- (%e ) - cos(x)%e )%e + %e + cos(x))sin(x) +--R + +--R - x 2 3 x - x 2 +--R (- cos(x)(%e ) + cos(x) - cos(x))%e + cos(x)%e - cos(x) + 1 +--R / +--R - x x 2 - x 2 2 x - x +--R 2%e %e sin(x) + (((%e ) - cos(x) + 1)%e + 2%e )sin(x) +--R + +--R - x 2 2 +--R (%e ) - cos(x) + 1 +--R Type: Expression Integer +--E 498 + +--S 499 of 578 +t0096:= exp(x)*cosh(x)*sinh(x)^2 +--R +--R +--R x 2 +--R (437) cosh(x)%e sinh(x) +--R Type: Expression Integer +--E 499 + +--S 500 of 578 +r0096:= -1/16*exp(-2*x)-1/16*exp(2*x)+1/32*exp(4*x)-1/8*x +--R +--R +--R 4x 2x - 2x +--R %e - 2%e - 2%e - 4x +--R (438) --------------------------- +--R 32 +--R Type: Expression Integer +--E 500 + +--S 501 of 578 +a0096:= integrate(t0096,x) +--R +--R +--R (439) +--R 3 2 2 3 +--R - 3sinh(x) + 3cosh(x)sinh(x) + (- 9cosh(x) - 4x + 2)sinh(x) + cosh(x) +--R + +--R (4x + 2)cosh(x) +--R / +--R 32sinh(x) - 32cosh(x) +--R Type: Union(Expression Integer,...) +--E 501 + +--S 502 of 578 +m0096:= a0096-r0096 +--R +--R +--R (440) +--R 3 2 +--R - 3sinh(x) + 3cosh(x)sinh(x) +--R + +--R 4x 2x - 2x 2 4x +--R (- %e + 2%e + 2%e - 9cosh(x) + 2)sinh(x) + cosh(x)%e +--R + +--R 2x - 2x 3 +--R - 2cosh(x)%e - 2cosh(x)%e + cosh(x) + 2cosh(x) +--R / +--R 32sinh(x) - 32cosh(x) +--R Type: Expression Integer +--E 502 + +--S 503 of 578 +d0096:= D(m0096,x) +--R +--R +--R (441) +--R 2 4x 2x - 2x 4x +--R - 6cosh(x)sinh(x) + (- %e + %e - %e + 1)sinh(x) + cosh(x)%e +--R + +--R 2x - 2x 3 +--R - cosh(x)%e + cosh(x)%e - 2cosh(x) + cosh(x) +--R / +--R 8sinh(x) - 8cosh(x) +--R Type: Expression Integer +--E 503 + +--S 504 of 578 +t0097:= f^(a+b*x+c*x^2)*sinh(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (442) sinh(e x + d x + c)f +--R Type: Expression Integer +--E 504 + +--S 505 of 578 +r0097:= -1/4*exp(1)^(-c+(d-b*log(f))^2/(4*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(d-b*log(f)+2*x*(e-c*log(f)))/(e-c*log(f))^(1/2))/_ + (e-c*log(f))^(1/2)+1/4*exp(1)^(c-(d+b*log(f))^2/(4*e+4*c*log(f)))*_ + f^a*%pi^(1/2)*erfi(1/2*(d+b*log(f)+2*x*(e+c*log(f)))/_ + (e+c*log(f))^(1/2))/(e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 505 + +--S 506 of 578 +a0097:= integrate(t0097,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (443) | sinh(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 506 + +--S 507 of 578 +m0097:= a0097-r0097 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (444) | sinh(%A e + %A d + c)f d%A - r0097 +--R ++ +--R Type: Expression Integer +--E 507 + +--S 508 of 578 +d0097:= D(m0097,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (445) sinh(e x + d x + c)f +--R Type: Expression Integer +--E 508 + +--S 509 of 578 +t0098:= f^(a+b*x+c*x^2)*cosh(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (446) cosh(e x + d x + c)f +--R Type: Expression Integer +--E 509 + +--S 510 of 578 +r0098:= 1/4*exp(1)^(-c+(d-b*log(f))^2/(4*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(d-b*log(f)+2*x*(e-c*log(f)))/_ + (e-c*log(f))^(1/2))/(e-c*log(f))^(1/2)+_ + 1/4*exp(1)^(c-(d+b*log(f))^2/(4*e+4*c*log(f)))*f^a*_ + %pi^(1/2)*erfi(1/2*(d+b*log(f)+2*x*(e+c*log(f)))/_ + (e+c*log(f))^(1/2))/(e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 510 + +--S 511 of 578 +a0098:= integrate(t0098,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (447) | cosh(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 511 + +--S 512 of 578 +m0098:= a0098-r0098 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (448) | cosh(%A e + %A d + c)f d%A - r0098 +--R ++ +--R Type: Expression Integer +--E 512 + +--S 513 of 578 +d0098:= D(m0098,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (449) cosh(e x + d x + c)f +--R Type: Expression Integer +--E 513 + +--S 514 of 578 +t0099:= 1/exp(x)/(1-exp(1)^(-2*x))^(1/2) +--R +--R +--R 1 +--R (450) ------------------ +--R +------------+ +--R x | - 2x +--R %e \|- %e + 1 +--R Type: Expression Integer +--E 514 + +--S 515 of 578 +r0099:= -arcsin(exp(-x)) +--R +--R There are no library operations named arcsin +--R Use HyperDoc Browse or issue +--R )what op arcsin +--R to learn if there is any operation containing " arcsin " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arcsin with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 515 + +--S 516 of 578 +a0099:= integrate(t0099,x) +--R +--R +--R +----------+ +--R | x 2 x +--R (451) 2atan(\|(%e ) - 1 - %e ) +--R Type: Union(Expression Integer,...) +--E 516 + +--S 517 of 578 +m0099:= a0099-r0099 +--R +--R +--R +----------+ +--R | x 2 x +--R (452) 2atan(\|(%e ) - 1 - %e ) - r0099 +--R Type: Expression Integer +--E 517 + +--S 518 of 578 +d0099:= D(m0099,x) +--R +--R +--R 1 +--R (453) ------------- +--R +----------+ +--R | x 2 +--R \|(%e ) - 1 +--R Type: Expression Integer +--E 518 + +--S 519 of 578 +t0100:= exp(x)/(-4+exp(1)^(2*x)) +--R +--R +--R x +--R %e +--R (454) -------- +--R 2x +--R %e - 4 +--R Type: Expression Integer +--E 519 + +--S 520 of 578 +r0100:= -1/2*arctanh(1/2*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 520 + +--S 521 of 578 +a0100:= integrate(t0100,x) +--R +--R +--R x x +--R - log(%e + 2) + log(%e - 2) +--R (455) ----------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 521 + +--S 522 of 578 +m0100:= a0100-r0100 +--R +--R +--R x x +--R - log(%e + 2) + log(%e - 2) - 4r0100 +--R (456) -------------------------------------- +--R 4 +--R Type: Expression Integer +--E 522 + +--S 523 of 578 +d0100:= D(m0100,x) +--R +--R +--R x +--R %e +--R (457) ---------- +--R x 2 +--R (%e ) - 4 +--R Type: Expression Integer +--E 523 + +--S 524 of 578 +t0101:= (exp(1)^(-2*x)+exp(1)^(2*x))/(-exp(1)^(-2*x)+exp(1)^(2*x)) +--R +--R +--R 2x - 2x +--R %e + %e +--R (458) ------------- +--R 2x - 2x +--R %e - %e +--R Type: Expression Integer +--E 524 + +--S 525 of 578 +r0101:= 1/2*log(-exp(-2*x)+exp(2*x)) +--R +--R +--R 2x - 2x +--R log(%e - %e ) +--R (459) ------------------ +--R 2 +--R Type: Expression Integer +--E 525 + +--S 526 of 578 +a0101:= integrate(t0101,x) +--R +--R +--R 2x 2 +--R log((%e ) - 1) - 2x +--R (460) --------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 526 + +--S 527 of 578 +m0101:= a0101-r0101 +--R +--R +--R 2x 2 2x - 2x +--R log((%e ) - 1) - log(%e - %e ) - 2x +--R (461) ------------------------------------------ +--R 2 +--R Type: Expression Integer +--E 527 + +--S 528 of 578 +d0101:= D(m0101,x) +--R +--R +--R - 2x 2x 2 2x +--R - 2%e (%e ) + 2%e +--R (462) --------------------------------------- +--R 2x 3 - 2x 2x 2 2x - 2x +--R (%e ) - %e (%e ) - %e + %e +--R Type: Expression Integer +--E 528 + +--S 529 of 578 +t0102:= exp(x)/(16-exp(1)^(2*x)) +--R +--R +--R x +--R %e +--R (463) - --------- +--R 2x +--R %e - 16 +--R Type: Expression Integer +--E 529 + +--S 530 of 578 +r0102:= 1/4*arctanh(1/4*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 530 + +--S 531 of 578 +a0102:= integrate(t0102,x) +--R +--R +--R x x +--R log(%e + 4) - log(%e - 4) +--R (464) --------------------------- +--R 8 +--R Type: Union(Expression Integer,...) +--E 531 + +--S 532 of 578 +m0102:= a0102-r0102 +--R +--R +--R x x +--R log(%e + 4) - log(%e - 4) - 8r0102 +--R (465) ------------------------------------ +--R 8 +--R Type: Expression Integer +--E 532 + +--S 533 of 578 +d0102:= D(m0102,x) +--R +--R +--R x +--R %e +--R (466) - ----------- +--R x 2 +--R (%e ) - 16 +--R Type: Expression Integer +--E 533 + +--S 534 of 578 +t0103:= exp(1)^(4*x)/(16+exp(1)^(8*x))^(1/2) +--R +--R +--R 4x +--R %e +--R (467) ------------ +--R +---------+ +--R | 8x +--R \|%e + 16 +--R Type: Expression Integer +--E 534 + +--S 535 of 578 +r0103:= 1/4*arcsinh(1/4*exp(4*x)) +--R +--R There are no library operations named arcsinh +--R Use HyperDoc Browse or issue +--R )what op arcsinh +--R to learn if there is any operation containing " arcsinh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arcsinh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 535 + +--S 536 of 578 +a0103:= integrate(t0103,x) +--R +--R +--R +------------+ +--R | 4x 2 4x +--R log(\|(%e ) + 16 - %e ) +--R (468) - --------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 536 + +--S 537 of 578 +m0103:= a0103-r0103 +--R +--R +--R +------------+ +--R | 4x 2 4x +--R - log(\|(%e ) + 16 - %e ) - 4r0103 +--R (469) -------------------------------------- +--R 4 +--R Type: Expression Integer +--E 537 + +--S 538 of 578 +d0103:= D(m0103,x) +--R +--R +--R 4x +--R %e +--R (470) --------------- +--R +------------+ +--R | 4x 2 +--R \|(%e ) + 16 +--R Type: Expression Integer +--E 538 + +--S 539 of 578 +t0104:= 1/exp(x)/(1+2*exp(x)) +--R +--R +--R 1 +--R (471) ------------- +--R x 2 x +--R 2(%e ) + %e +--R Type: Expression Integer +--E 539 + +--S 540 of 578 +r0104:= -exp(-x)+2*log(2+exp(-x)) +--R +--R +--R - x - x +--R (472) 2log(%e + 2) - %e +--R Type: Expression Integer +--E 540 + +--S 541 of 578 +a0104:= integrate(t0104,x) +--R +--R +--R x x x +--R 2%e log(2%e + 1) - 2x %e - 1 +--R (473) ------------------------------ +--R x +--R %e +--R Type: Union(Expression Integer,...) +--E 541 + +--S 542 of 578 +m0104:= a0104-r0104 +--R +--R +--R x x x - x - x x +--R 2%e log(2%e + 1) - 2%e log(%e + 2) + (%e - 2x)%e - 1 +--R (474) ------------------------------------------------------------ +--R x +--R %e +--R Type: Expression Integer +--E 542 + +--S 543 of 578 +d0104:= D(m0104,x) +--R +--R +--R - x 2 x 2 - x 2 x - x +--R - 2(%e ) (%e ) - (%e ) %e + %e + 2 +--R (475) ------------------------------------------- +--R - x x 2 - x x +--R (2%e + 4)(%e ) + (%e + 2)%e +--R Type: Expression Integer +--E 543 + +--S 544 of 578 +t0105:= exp(x)*sec(-1+exp(x))^3 +--R +--R +--R x x 3 +--R (476) %e sec(%e - 1) +--R Type: Expression Integer +--E 544 + +--S 545 of 578 +r0105:= 1/2*arctanh(sin(-1+exp(x)))+1/2*sec(-1+exp(x))*tan(-1+exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 545 + +--S 546 of 578 +a0105:= integrate(t0105,x) +--R +--R +--R (477) +--R x 2 x x 2 x +--R cos(%e - 1) log(sin(%e - 1) + 1) - cos(%e - 1) log(sin(%e - 1) - 1) +--R + +--R x +--R 2sin(%e - 1) +--R / +--R x 2 +--R 4cos(%e - 1) +--R Type: Union(Expression Integer,...) +--E 546 + +--S 547 of 578 +m0105:= a0105-r0105 +--R +--R +--R (478) +--R x 2 x x 2 x +--R cos(%e - 1) log(sin(%e - 1) + 1) - cos(%e - 1) log(sin(%e - 1) - 1) +--R + +--R x x 2 +--R 2sin(%e - 1) - 4r0105 cos(%e - 1) +--R / +--R x 2 +--R 4cos(%e - 1) +--R Type: Expression Integer +--E 547 + +--S 548 of 578 +d0105:= D(m0105,x) +--R +--R +--R (479) +--R x x 4 x x 2 x x 2 +--R 2%e sin(%e - 1) + (%e cos(%e - 1) - 2%e )sin(%e - 1) +--R + +--R x x 4 x x 2 +--R - %e cos(%e - 1) - %e cos(%e - 1) +--R / +--R x 3 x 2 x 3 +--R 2cos(%e - 1) sin(%e - 1) - 2cos(%e - 1) +--R Type: Expression Integer +--E 548 + +--S 549 of 578 +t0106:= exp(x)/(2+3*exp(x)+exp(1)^(2*x)) +--R +--R +--R x +--R %e +--R (480) --------------- +--R 2x x +--R %e + 3%e + 2 +--R Type: Expression Integer +--E 549 + +--S 550 of 578 +r0106:= -2*arctanh(3+2*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 550 + +--S 551 of 578 +a0106:= integrate(t0106,x) +--R +--R +--R x x +--R (481) - log(%e + 2) + log(%e + 1) +--R Type: Union(Expression Integer,...) +--E 551 + +--S 552 of 578 +m0106:= a0106-r0106 +--R +--R +--R x x +--R (482) - log(%e + 2) + log(%e + 1) - r0106 +--R Type: Expression Integer +--E 552 + +--S 553 of 578 +d0106:= D(m0106,x) +--R +--R +--R x +--R %e +--R (483) ----------------- +--R x 2 x +--R (%e ) + 3%e + 2 +--R Type: Expression Integer +--E 553 + +--S 554 of 578 +t0107:= 2^x/(1+4^x)^(1/2) +--R +--R +--R x +--R 2 +--R (484) --------- +--R +------+ +--R | x +--R \|4 + 1 +--R Type: Expression Integer +--E 554 + +--S 555 of 578 +r0107:= arcsinh(2^x)/log(2) +--R +--R There are no library operations named arcsinh +--R Use HyperDoc Browse or issue +--R )what op arcsinh +--R to learn if there is any operation containing " arcsinh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arcsinh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 555 + +--S 556 of 578 +a0107:= integrate(t0107,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 556 + +--S 557 of 578 +m0107:= a0107-r0107 +--R +--R +--R (485) - r0107 + a0107 +--R Type: Polynomial Integer +--E 557 + +--S 558 of 578 +d0107:= D(m0107,x) +--R +--R +--R (486) 0 +--R Type: Polynomial Integer +--E 558 + +--S 559 of 578 +t0108:= exp(1)^(3*x)/(-1+exp(1)^(2*x)) +--R +--R +--R 3x +--R %e +--R (487) -------- +--R 2x +--R %e - 1 +--R Type: Expression Integer +--E 559 + +--S 560 of 578 +r0108:= exp(x)-arctanh(exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 560 + +--S 561 of 578 +a0108:= integrate(t0108,x) +--R +--R +--R x x x +--R - log(%e + 1) + log(%e - 1) + 2%e +--R (488) ------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 561 + +--S 562 of 578 +m0108:= a0108-r0108 +--R +--R +--R x x x +--R - log(%e + 1) + log(%e - 1) + 2%e - 2r0108 +--R (489) --------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 562 + +--S 563 of 578 +d0108:= D(m0108,x) +--R +--R +--R x 3 +--R (%e ) +--R (490) ---------- +--R x 2 +--R (%e ) - 1 +--R Type: Expression Integer +--E 563 + +--S 564 of 578 +t0109:= exp((a+x)^2)/x^2-2*a*exp((a+x)^2)/x +--R +--R +--R 2 2 +--R x + 2a x + a +--R (- 2a x + 1)%e +--R (491) ---------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 564 + +--S 565 of 578 +r0109:= -exp((a+x)^2)/x+%pi^(1/2)*erfi(a+x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 565 + +--S 566 of 578 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 +--R x a + 2%A a + %A +--R ++ (- 2%A a + 1)%e +--R (492) | ------------------------------- d%A +--R ++ 2 +--R %A +--R Type: Union(Expression Integer,...) +--E 566 + +--S 567 of 578 +m0109:= a0109-r0109 +--R +--R +--R 2 2 +--R x a + 2%A a + %A +--R ++ (- 2%A a + 1)%e +--R (493) | ------------------------------- d%A - r0109 +--R ++ 2 +--R %A +--R Type: Expression Integer +--E 567 + +--S 568 of 578 +d0109:= D(m0109,x) +--R +--R +--R 2 2 +--R x + 2a x + a +--R (- 2a x + 1)%e +--R (494) ---------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 568 + +--S 569 of 578 +t0110:= 1/(-exp(x)+exp(1)^(3*x)) +--R +--R +--R 1 +--R (495) ---------- +--R 3x x +--R %e - %e +--R Type: Expression Integer +--E 569 + +--S 570 of 578 +r0110:= exp(-x)-arctanh(exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 570 + +--S 571 of 578 +a0110:= integrate(t0110,x) +--R +--R +--R x x x x +--R - %e log(%e + 1) + %e log(%e - 1) + 2 +--R (496) --------------------------------------- +--R x +--R 2%e +--R Type: Union(Expression Integer,...) +--E 571 + +--S 572 of 578 +m0110:= a0110-r0110 +--R +--R +--R x x x x x +--R - %e log(%e + 1) + %e log(%e - 1) - 2r0110 %e + 2 +--R (497) ---------------------------------------------------- +--R x +--R 2%e +--R Type: Expression Integer +--E 572 + +--S 573 of 578 +d0110:= D(m0110,x) +--R +--R +--R 1 +--R (498) ------------ +--R x 3 x +--R (%e ) - %e +--R Type: Expression Integer +--E 573 + +--S 574 of 578 +t0111:= 10^(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +--R \|x +--R 10 +--R (499) ------ +--R +-+ +--R \|x +--R Type: Expression Integer +--E 574 + +--S 575 of 578 +r0111:= 2^(1+x^(1/2))*5^(x^(1/2))/log(10) +--R +--R +--R +-+ +-+ +--R \|x + 1 \|x +--R 2 5 +--R (500) -------------- +--R log(10) +--R Type: Expression Integer +--E 575 + +--S 576 of 578 +a0111:= integrate(t0111,x) +--R +--R +--R +-+ +--R log(10)\|x +--R 2%e +--R (501) -------------- +--R log(10) +--R Type: Union(Expression Integer,...) +--E 576 + +--S 577 of 578 +m0111:= a0111-r0111 +--R +--R +--R +-+ +-+ +-+ +--R \|x + 1 \|x log(10)\|x +--R - 2 5 + 2%e +--R (502) --------------------------------- +--R log(10) +--R Type: Expression Integer +--E 577 + +--S 578 of 578 +d0111:= D(m0111,x) +--R +--R +--R +-+ +-+ +-+ +--R \|x + 1 \|x log(10)\|x +--R (- log(5) - log(2))2 5 + 2log(10)%e +--R (503) --------------------------------------------------------- +--R +-+ +--R 2log(10)\|x +--R Type: Expression Integer +--E 578 + +)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}